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.
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+26367 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.
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