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The sides of triangle $$XYZ$$ are $$XY = XZ = 25$$ and $$YZ = 40.$$ A semicircle is inscribed in triangle $$XYZ$$ so that its diameter lies on $$\overline{YZ}$$, and is tangent to the other two sides. Find the area of the semicircle.

Thank you very much for your help!

May 24, 2020

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The sides of triangle $$XYZ$$ are $$XY = XZ = 25$$ and $$YZ = 40$$.
A semicircle is inscribed in triangle $$XYZ$$ so that its diameter lies on line $$\overline{YZ}$$, and is tangent to the other two sides.
Find the area of the semicircle.

May 25, 2020