2023 AMC 12B Problems/Problem 3
Problem
A 3-4-5 right triangle is inscribed circle , and a 5-12-13 right triangle is inscribed in circle . What is the ratio of the area of circle to circle ?
Solution 1
Because the triangle 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: .
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