Circle O is tangent to AB at A, and angle ABD = 90 degrees. If AB = 12 and CD = 18, find the radius of the circle.
thanks to anyone who answers!
Let r be the radius of the circle.
Obviously, OC = r.
Let M be the mid-point of CD.
Since \(\angle ABD = 90^\circ\), ABMO is a rectangle. Therefore, OM = 12.
Since M is the midpoint of CD, CM = 18/2 = 9.
Then, by Pythagorean theorem,
\(OC^2 = OM^2 + MC^2\\ r^2 = 12^2 + 9^2 = 225\\ r = 15\)