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2023 AMC 12B Problem 3

Problem 3 of 25EasierGeometry

A 33-44-55 right triangle is inscribed in circle A,A, and a 55-1212-1313 right triangle is inscribed in circle B.B. What is the ratio of the area of circle AA to the area of circle B?B?

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Solution

The hypotenuse of an inscribed right triangle is a diameter, so circle AA has diameter 55 and circle BB has diameter 13.13. The ratio of areas is (513)2=25169.\left(\tfrac{5}{13}\right)^2= \tfrac{25}{169}. Thus, the correct answer is D.

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Concepts: right triangle · circle area · area ratio

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.