+1248 Semicircles are constructed on AB, AC, and BC. Find the radius of the circle.
AB = 10.
+36943 From the diagram below, using Pythagorean theorem:
2.5^2 + (5-r)^2 = (2.5+r)^2
6.25 + 25 - 10r + r^2 = 6.25 + 5 r + r^2
-15r = -25
r = 1 2/3 units ( and diameter = 2 * r = 3 1/3 units )
+36943 From the diagram below, using Pythagorean theorem:
2.5^2 + (5-r)^2 = (2.5+r)^2
6.25 + 25 - 10r + r^2 = 6.25 + 5 r + r^2
-15r = -25
r = 1 2/3 units ( and diameter = 2 * r = 3 1/3 units )
