{"id":"cb_question_bank:c2fe1960-f342-48d1-b55a-a5eb7f983f34","source_id":"cb_question_bank","source_item_id":"c2fe1960-f342-48d1-b55a-a5eb7f983f34","external_id":"fa02652e-89a4-4784-990e-fd5f06d65862","ibn":null,"question_id":"ae041e52","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A square is inscribed in a circle. The radius of the circle is StartFraction 20 StartRoot 2 EndRoot Over 2 EndFraction inches. What is the side length, in inches, of the square?","stimulus":"","stimulus_html":null,"stem_html":"

A square is inscribed in a circle. The radius of the circle is 2022 inches. What is the side length, in inches, of the square?

","rationale_html":"

Choice A is correct. When a square is inscribed in a circle, a diagonal of the square is a diameter of the circle. It's given that a square is inscribed in a circle and the length of a radius of the circle is 2022 inches. Therefore, the length of a diameter of the circle is 22022 inches, or 202 inches. It follows that the length of a diagonal of the square is 202 inches. A diagonal of a square separates the square into two right triangles in which the legs are the sides of the square and the hypotenuse is a diagonal. Since a square has 4\n congruent sides, each of these two right triangles has congruent legs and a hypotenuse of length 202 inches. Since each of these two right triangles has congruent legs, they are both 45\n-45\n-90\n triangles. In a 45\n-45\n-90\n triangle, the length of the hypotenuse is 2 times the length of a leg. Let s\n represent the length of a leg of one of these 45\n-45\n-90\n triangles. It follows that 202=2s. Dividing both sides of this equation by 2 yields 20=s. Therefore, the length of a leg of one of these 45\n-45\n-90\n triangles is 20\n inches. Since the legs of these two 45\n-45\n-90\n triangles are the sides of the square, it follows that the side length of the square is 20\n inches.

\n

Choice B is incorrect. This is the length of a radius, in inches, of the circle.

\n

Choice C is incorrect. This is the length of a diameter, in inches, of the circle.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.840000+00:00","source_updated_at":"2023-08-02T20:25:59.840000+00:00","options":[{"label":"A","content_html":"

20\n

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

2022

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

202

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

40\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}}