The sides of triangle XYZ are XY = XZ = 25 and YZ = 50. A semicircle is inscribed in triangle XYZ so that its diameter lies on YZ and is tangent to the other two sides. Find the area of the semicircle.

Such a triangle is not possible

By the triangle inequality :

XY + XZ must be greater than YZ

But

25 + 25 = 50 = YZ