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Semicircles are constructed on AB, AC, and BC.  A circle is tangent to all three semicircles.  Find the radius of the circle.

 

 Mar 19, 2024
 #1
avatar+128406 
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Here : https://web2.0calc.com/questions/semicircles_5

 

cool cool cool

 Mar 19, 2024
 #2
avatar+14903 
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Find the radius of the circle.

 

\((1+r)^2=1^2+(2-r)^2\\ 1+2r+r^2=1+4-4r+r^2\\ 6r=4\\ \color{blue}r=\frac{2}{3}\)

\(\color{blue}The\ radius\ of\ the\ circle\ is\  \frac{2}{3}.\)

laugh !

 Mar 19, 2024

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