OG详解-OG9 数学2 Q24

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 20√22​​ inches. Therefore, the length of a  diameter of the circle is 2(20√22) inches, or 20√2​ inches. It follows that the length of a diagonal of the square is 20√2inches. 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 these two right triangles has congruent legs and a hypotenuse of length 20√2​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 45-45-90 triangles. It follows that s 20​√2 = √2 (s). Dividing both sides of this  equation by √2​  yields 20=s. Therefore, the length of a leg of one of these 45-45-90 triangles is 20 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.