Geometry

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.

Answer by CPhill see here: https://web2.0calc.com/questions/geo-help-thank-you-stay-safe#r2

Let O be a center of a semicircle and T the tangent point on XY

∠XYO = arccos( YO / XY )

Radius  TO = sin( ∠XYO ) * YO 

Area = 1/2 (TO² *pi )