Let AB be a diameter of a circle, and let C be a point on the circle such that AC=8 and BC=14 The angle bisector of ACB intersects the circle at point M Find CM.
I'll give you some initial hints. First of all, angle ACB is 90 degrees because C lies on the circumference. So triangle ACB is a right triangle, thus CM makes a 45 degree angle with AC and BC, the radius of the circle is sqrt(65). How can you use trig or smarter methods to obtain CM?