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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