
633 F.3d 971 (2011)
Roozana Maria RITONGA; Nelson Estomihi Simanungkalit, Petitioners,
v.
Eric H. HOLDER, Jr., United States Attorney General, Respondent.
No. 09-9539.
United States Court of Appeals, Tenth Circuit.
January 28, 2011.
*973 David M. Haghighi of VHF Law Group, Los Angeles, CA, for Petitioners.
Thomas B. Fatouros, Senior Litigation Counsel, Office of Immigration Litigation, and Annette M. Wietecha, Office of Immigration Litigation, Civil Division, Washington, DC, for Respondent.
Before TYMKOVICH, SEYMOUR and BALDOCK, Circuit Judges.
SEYMOUR, Circuit Judge.
Roozana Maria Ritonga, joined by her husband Nelson Estomihi Simanungkalit, petitions for review of a final order of the Board of Immigration Appeals ("BIA") denying her application for asylum and restriction on removal under the Immigration and Nationality Act ("INA"), and request for protection under the United Nations Convention Against Torture ("CAT"). We have jurisdiction to review the BIA's final orders of removal, deportation, and exclusion under 8 U.S.C. § 1252(a). We deny Ms. Ritonga's petition.

I.
Ms. Ritonga was born and raised Christian in Indonesia. She testified that Muslims often screamed at and taunted her for being Christian when she was at school or leaving church. She attended school in England between 1991 and 1996. After completing her studies, she returned to Indonesia to work in the tourism industry.
In 1998, Indonesia experienced anti-Christian, anti-Chinese rioting. During this period of unrest, the lobby and restaurant of the hotel where Ms. Ritonga worked "were destroyed by Muslim radicals," although she was not at the hotel the day this occurred. Rec., vol. I at 133. During the riots, there was violence in the streets; stores and buildings near her home were robbed and set on fire. She feared her apartment building also would be burned.
Members of her family also were subject to violence during this period. For example, in 1997, two of her brothers were beaten. During the 1998 riots, her aunt's bakery was robbed and burned.
In 2000, three Muslims forced their way into Ms. Ritonga's home, asked her if she was a Christian, and broke and stole many of her possessions. They also pushed her against the wall, causing her head to bleed. The police arrived thereafter and apprehended the men. Ms. Ritonga sought medical attention for her head injury. On December 24 that year, Ms. Ritonga and her family were at church when a Catholic church nearby was bombed. Her church was spared because it had paid police to guard it. In March 2001, Ms. Ritonga was stopped in her car by a train at a railroad crossing. She testified that Muslim men, upon seeing a Christian cross in her car, hit the doors and windows of her car with clubs, trying to force her to get out of the car. She was able to escape without injury.
Before and after the riots, Ms. Ritonga made visits to the United States. She vacationed in the United States in 1990 and 1992, and returned home to Indonesia after each trip. In May 1999, she made a third trip to the United States to watch one of her brothers graduate. She again returned to Indonesia with her parents, with the expectation that she would not be living in Indonesia much longer. She believed her employer would allow her to transfer her job to a Singapore hotel. The transfer never occurred.
*974 Mr. Simanungkalit entered the United States on May 21, 2000, with permission to stay in the country until November 20, 2000. Ms. Ritonga entered the United States in June 2001 as a non-immigrant B2 visitor with authorization to remain in the United States until June 25, 2002. Ms. Ritonga and her husband overstayed their visas and remained in the United States without authorization, where they remain today.[1]
Ms. Ritonga timely filed her application for asylum and restriction on removal in June 2002, claiming she had been persecuted based on her Christian faith. Ms. Ritonga's parents and two of her four siblings still live in Indonesia. One sibling now lives in Singapore; another lives in the United States.
In his review of Ms. Ritonga's asylum petition, the Immigration Judge ("IJ") found she lacked credibility, in part because she returned to Indonesia after trips to England and the United States. On appeal, the BIA rejected the IJ's determination that Ms. Ritonga was not credible. Nevertheless, even accepting Ms. Ritonga's claims at face value, the BIA determined that she failed to meet her burden of proof for asylum or restriction on removal. Ms. Ritonga has petitioned for our review.

II.
The scope of our review is governed by the form of the BIA decision. Sidabutar v. Gonzales, 503 F.3d 1116, 1122-23 (10th Cir.2007). Where the BIA issues its own opinion dismissing the appeal in a single-member decision pursuant to 8 C.F.R. § 1003.1(e)(5), the order "constitutes the final order of removal under 8 U.S.C. § 1252(a)." Uanreroro v. Gonzales, 443 F.3d 1197, 1204 (10th Cir.2006) (citation omitted). Although we review the BIA's opinion, we also may consult the IJ's explanation. Id. This is especially appropriate in three circumstances:
(1) where the BIA incorporates by reference the IJ's rationale, (2) where the BIA repeats a condensed version of [the IJ's] reasons while also relying on the IJ's more complete discussion, and (3) where the BIA reasoning is difficult to discern and the IJ's analysis is all that can give substance to the BIA's reasoning.
Sarr v. Gonzales, 474 F.3d 783, 790 (10th Cir.2007) (quoting Uanreroro, 443 F.3d at 1204) (internal quotation marks omitted) (alteration in original).
In our review of the agency's decision, we decide purely legal questions de novo. Elzour v. Ashcroft, 378 F.3d 1143, 1150 (10th Cir.2004). Agency findings of fact are reviewed under the substantial evidence standard. Id. Under this standard of review, agency "findings of fact are conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary." 8 U.S.C. § 1252(b)(4)(B). In this circuit, the "determination whether an alien has demonstrated persecution is a question of fact. . . ." Hayrapetyan v. Mukasey, 534 F.3d 1330, 1335 (10th Cir.2008) (internal quotation marks omitted).
"[O]ur review is confined to the reasoning given by the [agency], and we will not independently search the record for alternative bases to affirm." Elzour, 378 F.3d at 1150; see also SEC v. Chenery Corp., 332 U.S. 194, 196, 67 S.Ct. 1575, 91 *975 L.Ed. 1995 (1947) (explaining that a court "must judge the propriety of [agency] action solely by the grounds invoked by the agency").

A. Asylum
To be eligible for a discretionary grant of asylum by the Attorney General, an alien must first establish she is a refugee. 8 U.S.C. § 1158(b)(1)(A). A refugee is an individual who is "outside" the country of his or her nationality, and "is unable or unwilling to return to . . . that country because of persecution or a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion." 8 U.S.C. § 1101(a)(42)(A).[2] A petitioner can establish refugee status by establishing either "past persecution" or a "well-founded fear of future persecution." 8 C.F.R. § 1208.13(b).

1. Past Persecution
Persecution is "the infliction of suffering or harm upon those who differ (in race, religion, or political opinion) in a way regarded as offensive and must entail more than just restrictions or threats to life and liberty. Such persecution may be inflicted by the government itself, or by a non-governmental group that the government is unwilling or unable to control." Wiransane v. Ashcroft, 366 F.3d 889, 893 (10th Cir.2004) (internal quotation marks and citations omitted). We do not look at each incident in isolation, but instead consider them collectively, because the cumulative effects of multiple incidents may constitute persecution. See Witjaksono v. Holder, 573 F.3d 968, 977 (10th Cir.2009) (considering incidents cumulatively); see also Fei Mei Cheng v. Att'y Gen. of the U.S., 623 F.3d 175, 192 (3d Cir.2010) (holding that "incidents alleged to constitute persecution . . . must be considered cumulatively" (alteration in original) (internal quotation marks omitted)); Chen v. Holder, 604 F.3d 324, 333-34 (7th Cir.2010) (similar); Ngengwe v. Mukasey, 543 F.3d 1029, 1036 (8th Cir.2008) (similar); Delgado v. U.S. Att'y Gen., 487 F.3d 855, 861 (11th Cir.2007) (similar); Edimo-Doualla v. Gonzales, 464 F.3d 276, 283 (2d Cir. 2006) (similar); Korablina v. INS, 158 F.3d 1038, 1044 (9th Cir.1998) (similar).
The BIA held that although Ms. Ritonga was credible, there was "no error in the Immigration Judge's alternate determination that the respondent failed to meet her burden of proof for the requested relief." Rec., vol. I at 3. Ms. Ritonga disputes that the IJ made such an alternative finding, which would have accepted her testimony at face value. Consequently, she contends the BIA erred by affirming the IJ's denial of asylum without "support[ing] its decision with any independent facts or analysis." Aplt. Br. at 15.
Although Ms. Ritonga correctly characterizes the IJ's opinion, we are not persuaded the BIA provided insufficient analysis and findings to support its decision. The opinion, taken as a whole, provides sufficient findings and analysis to facilitate our review. See Becerra-Jimenez v. INS, 829 F.2d 996, 1000 (10th Cir. 1987) ("What is required is merely that [the BIA] consider the issues raised, and announce its decision in terms sufficient to enable a reviewing court to perceive that it has heard and thought and not merely reacted." (internal quotation marks omitted)). Here, the BIA explained, "the respondent's assertions, even taken at face value, did not make out a claim of either *976 past persecution or a well-founded fear of persecution on account of a protected ground." Rec., vol. I at 4. After reviewing the record, we conclude the BIA's determination that Ms. Ritonga failed to establish past persecution is supported by substantial evidence.
We have previously reviewed appeals by Christian Indonesians seeking asylum and restriction on removal. See, e.g., Witjaksono, 573 F.3d 968; Sidabutar v. Gonzales, 503 F.3d 1116 (10th Cir.2007); Tulengkey v. Gonzales, 425 F.3d 1277 (10th Cir.2005). In Witjaksono, the petitioner described incidents in which he was targeted for being Christian and/or Chinese. Muslim students taunted him and threw rocks at him for being Chinese, a group attacked his car while he was stopped at a traffic light, a soldier assaulted him, a church in his neighborhood was bombed, and he hid in his home during the 1998 riots. 573 F.3d at 972-73. We affirmed the determination that he failed to demonstrate past persecution. Id. at 977.
Similar facts require the same conclusion in this case. Just as in Witjaksono, Ms. Ritonga suffered minor injuries only once, when Muslims broke into her home. But as the lone occasion in her life in which she was physically injured, we cannot say this constituted persecution within the meaning of the statute. See id. Additionally, the police investigated the assault and apprehended the criminals, which undermines Ms. Ritonga's argument that the government was "unwilling or unable to control" the perpetrators. See Wiransane, 366 F.3d at 893. Muslims also attacked her car while she was inside of it, but she suffered no injuries. These events do not necessarily rise to the level of persecution. See Sidabutar, 503 F.3d at 1124-25 (finding no past persecution when a Christian Indonesian was beaten repeatedly by Muslim classmates for his religion and had his motorcycle burned).
Similarly, Ms. Ritonga's descriptions of the 1998 riots and the church bombing are insufficient to establish persecution. See Witjaksono, 573 F.3d at 977 ("Witjaksono's descriptions of the 1998 Jakarta riots and the 1999 church bombing do not mandate relief."). Ms. Ritonga does not suggest that she was individually targeted or physically harmed in these events. See id. We do not doubt these experiences were frightening for Ms. Ritonga and her family. Even considering all of these incidents cumulatively, however, we cannot conclude that a reasonable adjudicator would be compelled to find Ms. Ritonga suffered past persecution, given our prior decisions in analogous circumstances.

2. Well-Founded Fear of Future Persecution
Having failed to prove past persecution, Ms. Ritonga still could gain refugee status by demonstrating a well-founded fear of future persecution. See 8 C.F.R. § 1208.13(b). For a fear of future persecution to be well-founded, it must be both "subjectively genuine and objectively reasonable." Tulengkey, 425 F.3d at 1281. Such a fear is objectively well-founded if (1) the petitioner "may be singled out for persecution upon returning to her country of origin or (2) `there is a pattern or practice in [that] country . . . of persecution of a group of persons similarly situated to the applicant'" on account of a protected classification. Id. (quoting 8 C.F.R. § 208.13(b)(2)(iii)) (alterations in original). For asylum purposes, "it need not be shown that the situation will probably result in persecution, but it is enough that persecution is a reasonable possibility." INS v. Cardoza-Fonseca, 480 U.S. 421, 440, 107 S.Ct. 1207, 94 L.Ed.2d 434 (1987). Fear of persecution is not well-founded if *977 the applicant can avoid persecution by relocating to another part of the country and it would be reasonable to expect her to do so. 8 C.F.R. § 1208.13(b)(2)(ii), (b)(3). Ms. Ritonga does not argue that she would be singled out for persecution if she returned to Indonesia, so we consider whether the record compels the conclusion that there is a pattern or practice of persecution of Christians in Indonesia.
According to Ms. Ritonga, the BIA's affirmation of the IJ's decision must be rejected because the IJ failed to support his determination that she lacked a well-founded fear of persecution with any facts. We disagree. The IJ repeatedly referenced facts from State Department reports which support his finding. Even if the IJ did not go into as much detail as Ms. Ritonga would like, the record provides substantial evidence to support his finding, and he announced his decision in terms sufficient to enable our review. See Witjaksono, 573 F.3d at 978.
The BIA determined Ms. Ritonga lacked a well-founded fear of persecution for several reasons. First, Ms. Ritonga's repeated returns to Indonesia even after the riots had occurred undermined her claim of subjective fear of living in the country. Furthermore, the objective reasonableness of her fear is "undermined by the fact that most of her family remains in Indonesia unharmed." Rec., vol. I at 3. The BIA also ruled that Ms. Ritonga failed to establish a pattern or practice of continuing persecution against Christians in Indonesia sufficient to demonstrate that her fear is objectively well-founded. See 8 C.F.R. § 208.13(b)(2)(iii)(A); see also Tulengkey, 425 F.3d at 1281.
We agree with the BIA that Ms. Ritonga's repeated returns to Indonesia, as well as the continued presence of her family in Indonesia without further violent incidents, undercuts her asserted fear of persecution. See Hakeem v. INS, 273 F.3d 812, 816-17 (9th Cir.2001), superceded on other grounds by Real ID Act of 2005, Pub.L. No. 109-13, 119 Stat. 231 (codified as amended at 8 U.S.C. § 1252(a)(2)(D)); Melgar de Torres v. Reno, 191 F.3d 307, 313 (2d Cir.1999).
Moreover, Ms. Ritonga has failed to demonstrate the BIA erred in finding that she could reasonably relocate within the country. The IJ explained, "there are areas in Indonesia that are strictly or majority Christians, [sic] so there are places that [Ms. Ritonga] could have relocated if she wished." Rec., vol. I at 100. Indeed, Ms. Ritonga's family resides on North Sumatra, an island that is primarily Christian.
Ms. Ritonga asserts the record "plainly demonstrates that the government is . . . unable or unwilling to stem the tide of violence against Christians in Indonesia. . . ." Aplt. Br. at 18. It is true that she submitted voluminous documentation of violence against Christians in various parts of Indonesia over the years, including newspaper articles and material from websites.[3] Indeed, the State Department International Religious Freedom Report 2007 on Indonesia documents that the Indonesian government "sometimes tolerated discrimination against and the abuse of religious groups by private actors and often failed to punish perpetrators." Rec., vol. I at 185. The Report also notes, however, that "government policy continued to contribute to the generally free *978 practice of religion." Id. The State Department International Religious Freedom Report for 2006 indicates the government was actively prosecuting those who perpetrated religiously-motivated crimes. That report also states that the Indonesian government was working with Muslim and Christian community leaders to defuse religious conflict, and that religiously-motivated violence in parts of the country was declining. The record as a whole reflects there are problems of violence in Indonesia, as well as discrimination against Christians, but the government overall does not seem unable or unwilling to combat such crimes. Sporadic incidents of violence do not necessarily compel the conclusion that there is a "pattern or practice" of persecution against Christians in Indonesia. See, e.g., Tulengkey, 425 F.3d at 1281-82 (Christian Indonesians failed to show relocation within Indonesia was unreasonable).
Ms. Ritonga has not convinced us the BIA denied her asylum petition contrary to the weight of the evidence. Although the record illustrates religious problems in Indonesia, we cannot conclude the weight of the evidence is so overwhelming that an adjudicator would be compelled to find a well-founded fear of persecution.

B. Restriction on Removal
To be eligible for restriction on removal under the INA, an applicant must demonstrate that her "life or freedom would be threatened in th[e] country [proposed for removal] because of [her] race, religion, nationality, membership in a particular social group or political opinion." 8 U.S.C. § 1231(b)(3)(A); see also Tulengkey, 425 F.3d at 1280. The applicant must show either past persecution in the proposed country of removal, or that "it is more likely than not that he or she would be persecuted" on one of the specified grounds upon returning to the proposed country of removal. 8 C.F.R. § 1208.16(b)(2); see also Sidabutar, 503 F.3d at 1123-24. The test for restriction on removal "is therefore more demanding than the `well-founded fear' standard applicable to an asylum claim." Elzour, 378 F.3d at 1149 (internal quotation marks omitted). As a result, an applicant who fails to satisfy the asylum eligibility requirement necessarily fails to qualify for restriction on removal. Uanreroro, 443 F.3d at 1202. Because we affirm the BIA's denial of her asylum petition, we also must hold that Ms. Ritonga failed to prove her eligibility for restriction on removal.

C. Convention Against Torture
To receive the protections of the CAT, an applicant must demonstrate "it is more likely than not that he or she would be tortured if removed to the proposed country of removal." 8 C.F.R. § 1208.16(c)(2). "A claim under the CAT differs from a claim for asylum or restriction on removal under the INA because there is no requirement that the petitioner show that torture will occur on account of a statutorily protected ground." Cruz-Funez v. Gonzales, 406 F.3d 1187, 1192 (10th Cir.2005). Instead, it requires that she establish the treatment of her would be so severe as to constitute torture. Elzour, 378 F.3d at 1150. Such torture must be "by or at the instigation of or with the consent or acquiescence of a public official or other person acting in an official capacity." 8 C.F.R. § 1208.18(a)(1).
Ms. Ritonga argues the IJ and BIA improperly conflated her request for protection under the CAT with her requests for other forms of relief under the INA. We disagree. The BIA's analysis of the CAT claim is sparse, but the BIA "has no duty to write an exegesis on every contention." Witjaksono, 573 F.3d at 978 (internal *979 quotation marks omitted). The BIA correctly stated the legal standards applicable to each claim, see id., and explained Ms. Ritonga "failed to demonstrate that it is more likely than not that she would be tortured if returned to Indonesia." Rec., vol. I at 4.
In addition, Ms. Ritonga provided no evidence that her risks of persecution and torture differ. Instead, she relied on the same incidents to support her asylum and CAT claims. Because substantial evidence supports the BIA's finding that it is unlikely Ms. Ritonga would face future persecution if returned to Indonesia, "it is likewise against the odds that [she] would be tortured by the government or a proxy for the government." Sidabutar, 503 F.3d at 1126. Accordingly, we affirm the BIA's denial of relief under the CAT.
For the foregoing reasons, we DENY Ms. Ritonga's petition for review.
NOTES
[1]  Mr. Simanungkalit, also an Indonesian Christian, initially filed a separate asylum application, but it was deemed to be untimely. As a result, he is relying on his wife's asylum petition for relief. See 8 U.S.C. § 1158(b)(3) (allowing the spouse or child of an alien to be granted the same status as the alien in the asylum proceedings).
[2]  Although in special circumstances an individual does not need to be outside the country of his or her nationality to obtain refugee status, see 8 U.S.C. § 1101(a)(42)(B), such circumstances are not present in the instant case.
[3]  Ms. Ritonga's brief also quotes extensively from the 2007 Country Reports on Human Rights Practices for Indonesia prepared by the State Department. Because this material was not included in the record, we decline to consider it in our decisionmaking. See 8 U.S.C. § 1252(b)(4)(A) ("[T]he court of appeals shall decide the petition only on the administrative record on which the order of removal is based.").
