Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.
Here : https://web2.0calc.com/questions/semicircles_5
Find the radius of the circle.
\((1+r)^2=1^2+(2-r)^2\\ 1+2r+r^2=1+4-4r+r^2\\ 6r=4\\ \color{blue}r=\frac{2}{3}\)
\(\color{blue}The\ radius\ of\ the\ circle\ is\ \frac{2}{3}.\)
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