{"id":"cb_question_bank:3bd841d0-39f4-4ac6-bf49-de9879a7396c","source_id":"cb_question_bank","source_item_id":"3bd841d0-39f4-4ac6-bf49-de9879a7396c","external_id":null,"ibn":"11305-DC","question_id":"69b0d79d","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Point O is the center of the circle above, and the measure of angle O A, B is 30 degrees . If the length of line segment O C is 18, what is the length of arc A, B ?","stimulus":"The figure presents a circle with center O. Point A, lies on the upper left part of the circle. Point B lies on the upper right part of the circle. Point C is indicated at the bottom of the circle, directly below the center O. Line segment O A, line segment O B, and horizontal line segment A, B are drawn forming triangle O A, B. Vertical line segment O C is drawn.","stimulus_html":"
\n
\n \"The
\n
\n","stem_html":"

Point O is the center of the circle above, and the measure of \"angle is \"30. If the length of \"line is 18, what is the length of arc \"A,?

\n","rationale_html":"

Choice B is correct. Because segments OA and OB are radii of the circle centered at point O, these segments have equal lengths. Therefore, triangle AOB is an isosceles triangle, where angles OAB and OBA are congruent base angles of the triangle. It’s given that angle OAB measures \"30. Therefore, angle OBA also measures \"30. Let \"x represent the measure of angle AOB. Since the sum of the measures of the three angles of any triangle is \"180, it follows that \"30, or \"60. Subtracting \"60 from both sides of this equation yields \"x, or \"the radians. Therefore, the measure of angle AOB, and thus the measure of arc \"A,, is \"the radians. Since \"the is a radius of the given circle and its length is 18, the length of the radius of the circle is 18. Therefore, the length of arc \"A, can be calculated as \"the, or \"12.

Choices A, C, and D are incorrect and may result from conceptual or computational errors.

\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.639000+00:00","source_updated_at":"2023-08-02T20:25:59.639000+00:00","options":[{"label":"A","content_html":"

\n \n \"9\n

\n","ord":0},{"label":"B","content_html":"

\n \n \"12\n

\n","ord":1},{"label":"C","content_html":"

\n \n \"15\n

\n","ord":2},{"label":"D","content_html":"

\n \n \"18\n

\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}}