circles and triangles problem

Hi, everybody, i would like to use your help with thease two problems:

1. there is a regular triangle ABC drawn in the circle. one point D is chosen on the arch AB. prove that AD+DB=DC.

2. there is a triangle ABC and BD is a median. point T is on the BC.
BD and AT crosses in point M. calculate

1. By Ptolemy's theorem( Ptolemy's theorem - Wikipedia, the free encyclopedia ), we have: AB.CD = AD.BC + BD.AC.

Since the triangle is equilateral, AB = BC = AC. So these cancel out in the above equation to give us the result.