+1633 Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.
+130313 Let D be the center of the red circle and r its radius
Let E be the center of the semi-circle with BC as a diameter
The radius of the large semi-circle = 2
We can form right triangle BDE with BD = 2-r , BE = 1 and the hypotenuse = ED = 1 + r
So
2^2 + (2-r)^2 = (1 + r)^2
4 + 4 - 4r + r^2 = 1 + 2r + r^2
7 = 6r
r = 7/6
