Using Pythagoras' Theorem (see Hint in above diagram)

for the right-angled triangle in the figure alongside,

(r - a)^2 + (r - b)^2 = r^2

Now, a = 6 cm and b = 12 cm. So,

(r - 6)^2 + (r - 2)^2 = r^2 or

r^2 - 2(6)r + 36 + r^2 - 2(12)r + 144 = r^2. This simplifies to

r^2 - 36r + 180 = 0. On factorizing, we get

(r - 30)(r - 6) = 0.

Thus, **the radius of the circle is 30 cm**.