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
25 + 25 = 50 = YZ