{"id":"cb_practice_pdf:t9-math-m2-q24","source_id":"cb_practice_pdf","source_item_id":"t9-math-m2-q24","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-9","module_number":2,"position":24,"stem":"A square is inscribed in a circle. The radius of the circle is (20 2)/2 inches. What is the side length, in inches, of the square? 20","stimulus":"","stimulus_html":null,"stem_html":"<p>A square is inscribed in a circle. The radius of the circle is (20 2)/2 inches. What is the side length, in inches, of the square? 20</p>","rationale_html":"<p>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 20 2 and the length of a radius of the circle is 2 inches. Therefore, the length of a 2 20 2 20 2 diameter of the circle is c 2 m inches, or inches. It follows that the length 20 2 of a diagonal of the square is 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 congruent sides, each of 20 2 these two right triangles has congruent legs and a hypotenuse of length inches. Since each of these two right triangles has congruent legs, they are both 45-45-90 triangles. In a 45-45-90 triangle, the length of the hypotenuse is 2 times the length of a leg. Let s represent the length of a leg of one of these 20 2= 2 45-45-90 triangles. It follows that ^sh. Dividing both sides of this 20= equation by 2 yields s. Therefore, the length of a leg of one of these 20 45-45-90 triangles is inches. Since the legs of these two 45-45-90 triangles are the sides of the square, it follows that the side length of the square is 20 inches. Choice B is incorrect. This is the length of a radius, in inches, of the circle. Choice C is incorrect. This is the length of a diameter, in inches, of the circle. Choice D is incorrect and may result from conceptual or calculation errors. 46 SAT PRACTICE TEST #9 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"","ord":0},{"label":"B","content_html":"<p>(20 2)/2 20 2</p>","ord":1},{"label":"C","content_html":"<p>40</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}