I would be very grateful if you can help me with this problem. I've constructed the median ON, N ∈ BC, and I was able to find that the triangle OCN is isosceles (height and median coincide). Probably I have to prove it is equilateral, and the only way I can think of it is to show that there is an angle 60 degrees. I can't find a way to do it. Thanks in advance!
ABCD (AB || CD) is a rectangular trapeze, AD ⊥ AB. A circle with center midpoint O of AD is in contact with BC at M (touching). If AB = 36 cm CD = 12 cm, find the length of OC.