+0 Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.
+129771 Let D be the center of the circle and let its radius = r
Let E be the center of one of the small semi-circles
We can construct right triangle BDE with EBD = 90°
BE = 1
BD = 2 - r
ED = 1 + r
BE^2 + BD^2 = ED^2
1^1 + (2 -r)^2 = (1 + r)^2
1 + r^2 - 4r + 4 = r^2 + 2r + 1
6r = 4
r = 4/6 = 2/3
