Ab is tangent to circle c. find the radius r.

What a neat little problem
a^2 + b^2 = c^2
a = r
b = 15
c = r + 9

r^2 + 15^2= (r + 9)^2
r^2 + 225 = r^2 + 18r + 81 the r^2 cancel out
225 = 18r + 81 subtract 81 from both sides
144 = 18r divide by 18
144/18 = r
8 = r