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The longer base of an isosceles trapezoid is a chord of a circle, and the shorter base is tangent to the circle.  If the length of one leg is 5 and the lengths of the bases are 24 and 18, find the area of the circle.

 Dec 13, 2019
 #1
avatar+9097 
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The longer base of an isosceles trapezoid is a chord of a circle, and the shorter base is tangent to the circle. If the length of one leg is 5 and the lengths of the bases are 24 and 18, find the area of the circle.

 

Hello Guest!

 

\(h_{Tr}=\sqrt{5^2-3^2}=4\\ r^2=(r-h)^2+12^2\\ r^2=(r-4)^2+144=16-8r+r^2+144\\ 8r=160\\ \color{blue}r=20 \)

\(A=\pi r^2=\pi \cdot20^2\\ \color{blue} A= 1256.637\)

laugh  !

 Dec 13, 2019
edited by asinus  Dec 13, 2019
edited by asinus  Dec 13, 2019
 #2
avatar+11646 
+2

Here's the graphic.

laugh

 Dec 13, 2019

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