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smc

geometry senior

Problem

A right triangle is inscribed in circle , and a right triangle is inscribed in circle . What is the ratio of the area of circle to the area of circle ?
(A)
(B)
(C)
(D)
Solution
Because the triangles are right triangles, we know the hypotenuses are diameters of circles and . Thus, their radii are 2.5 and 6.5 (respectively). Square the two numbers and multiply to get and as the areas of the circles. Multiply 4 on both numbers to get and . Cancel out the , and lastly, divide, to get your answer
Final answer
D