{"id":"cb_question_bank:56835509-7047-41fb-b035-b92003046ec4","source_id":"cb_question_bank","source_item_id":"56835509-7047-41fb-b035-b92003046ec4","external_id":null,"ibn":"025406-DC","question_id":"ab176ad6","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation open parenthesis, x plus 6, close parenthesis, squared, plus, open parenthesis, y plus 3, close parenthesis, squared, equals 121 defines a circle in the xy ‑plane. What is the radius of the circle?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8b019e349d724547045749324ed08787f99434993af6dd963088d01a7db084d9\" alt=\"open parenthesis, x plus 6, close parenthesis, squared, plus, open parenthesis, y plus 3, close parenthesis, squared, equals 121 \"></span></span> defines a circle in the <span class=\"italic \">xy</span>‑plane. What is the radius of the circle?</p>\n","rationale_html":"<p>The correct answer is 11. A circle with equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9cc3ea1a80aa58d20d3505664d1795bea993c46ae0ac5896bf691ea90b2cae96\" alt=\"open parenthesis, x minus a, close parenthesis, squared, plus, open parenthesis, y minus b, close parenthesis, squared, equals r squared\"></span>, where <span class=\"italic\">a</span>, <span class=\"italic\">b,</span> and <span class=\"italic\">r</span> are constants, has center <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7438d2fd6d3cd4feef783fa625560d22e6e8048ef5358ea151bcda055a6b74a\" alt=\"with coordinates a, comma b\"></span> and radius <span class=\"italic\">r</span>. Therefore, the radius of the given circle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8667829ec7be2e2050700b653da0669cdefbd302c1ba5537d8d8671ad5fa74b0\" alt=\"the square root of 121\"></span>, or 11.</p>\n","correct_answer":["11"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+00:00","options":[],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}