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Problem 659

AMC 10/12, early questions

Geometry Difficulty 3.0 Prove it UKMT Senior Kangaroo · United Kingdom · 2021

On each side of a right-angled triangle, a semicircle is drawn with that side as a diameter. The areas of the three semicircles are $x^2$ , $3x$ and $180$ where $x^2$ and $3x$ are both less than $180$ . What is the area of the smallest semicircle?

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