+1725 Semicircles are constructed on AB, AC, and BC. Find the radius of the circle.
AB = 10.
+129771 Let O be the midpoint of MB......this is also the center of the the semi-circle on the right
MO = AB / 4 = 10/4 = 2.5
MC = 5 - r where 5 is the radius of the large semi-circle and r is the radius of the circle
CO = 2.5 + r
We have a right triangle such that
MC^2 + MO^2 = CO^2
(5 - r)^2 + 2.5^2 = (2.5 + r)^2
r^2 -10r + 25 + 6.25 + r^2 + 5r + 6.25
-10r + 25 = 5r
15r = 25
r = 25/15 = 5/3
