{"id":"cb_question_bank:95c2ee68-09ce-4d8a-978f-d143eb3e17e0","source_id":"cb_question_bank","source_item_id":"95c2ee68-09ce-4d8a-978f-d143eb3e17e0","external_id":null,"ibn":"08358-DC","question_id":"23c5fcce","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The circle above with center O has a circumference of 36. What is the length of minor arc A, C ?","stimulus":"The figure presents a circle with center O. Points A, and C are indicated on the circle, creating minor arc A, C. A diameter is drawn from point A to a point on the other side of the circle. Similarly, a diameter is drawn from point C to a point on the other side of the circle. The two lines intersect at the origin, forming a right angle at angle A, O C","stimulus_html":"<div class=\"stimulus_reference \">\n\t<div class=\"standalone_image \"><img src=\"/api/assets/20dd9b37949cf9cb41b55ee1fb6f3e527821081616445b1e65a0543af502b4c8\" alt=\"The figure presents a circle with center O. Points A, and C are indicated on the circle, creating minor arc A, C. A diameter is drawn from point A to a point on the other side of the circle. Similarly, a diameter is drawn from point C to a point on the other side of the circle. The two lines intersect at the origin, forming a right angle at angle A, O C\" width=\"82\" height=\"82\"></div>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">The circle above with center <span class=\"italic\">O</span> has a circumference of 36. What is the length of minor arc <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/63edf02716e59a1773858e42950af7a4cc0b9219969a224ffafd0de72c862a75\" alt=\"A, C\"></span>?</p>\n","rationale_html":"<p>Choice A is correct. A circle has 360 degrees of arc. In the circle shown, <span class=\"italic\">O</span> is the center of the circle and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/36d3fb5a5ad6048a778cd0528a442a853133dd74b0c443a0d9bfa93282f9f69e\" alt=\"angle A, O C\"></span> is a central angle of the circle. From the figure, the two diameters that meet to form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/36d3fb5a5ad6048a778cd0528a442a853133dd74b0c443a0d9bfa93282f9f69e\" alt=\"angle A, O C\"></span> are perpendicular, so the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/36d3fb5a5ad6048a778cd0528a442a853133dd74b0c443a0d9bfa93282f9f69e\" alt=\"angle A, O C\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64b4e01c27ff4e364299d314f9281e888bdd01137e9c7d6278e5c64f862aeb4c\" alt=\"90 degrees\"></span>. Therefore, the length of minor arc <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/63edf02716e59a1773858e42950af7a4cc0b9219969a224ffafd0de72c862a75\" alt=\"A, C\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1d9ef8ea17925e18d9e02c8262ee38ffbae1ab236b7e5255f828dfac940cc72d\" alt=\"the fraction 90 over 360\"></span> of the circumference of the circle. Since the circumference of the circle is 36, the length of minor arc <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/63edf02716e59a1773858e42950af7a4cc0b9219969a224ffafd0de72c862a75\" alt=\"A, C\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c7096c9cf4956032adb28777dc99817a98faccddddae0dc126501ade24a15cf6\" alt=\"the fraction 90 over 360, end fraction, times 36, equals 9\"></span>.</p><p>Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/63edf02716e59a1773858e42950af7a4cc0b9219969a224ffafd0de72c862a75\" alt=\"A, C\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c2cdda43637be35379a891f9cbba6a665ae6aa43f563929757acf84127e4bcef\" alt=\"one fourth\"></span> of the circumference. However, the lengths in choices B and C are, respectively, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fce26b7f770543c2e33190a4ea311aa1f4d8da39df9b43ef0ea5dfff882a8571\" alt=\"one third\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span> the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c2cdda43637be35379a891f9cbba6a665ae6aa43f563929757acf84127e4bcef\" alt=\"one fourth\"></span> the circumference.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"<p><span class=\"phantom_text \">9</span></p>\n","ord":0},{"label":"B","content_html":"<p>12</p>\n","ord":1},{"label":"C","content_html":"<p>18</p>\n","ord":2},{"label":"D","content_html":"<p>36</p>\n","ord":3}],"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}}