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# Geometry

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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
+26222
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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.

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

Aug 10, 2020
#2
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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 )

Aug 10, 2020