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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.

 Aug 10, 2020
 #1
avatar+25598 
+2

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

 

laugh

 Aug 10, 2020
 #2
avatar+1421 
+3

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 )  smiley

 Aug 10, 2020

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