Problems

Age
Difficulty
Found: 6

The point D lies on the base AC of the isosceles triangle ABC. Prove that the radii of the circumscribed circles of the triangles ABD and CBD are equal.

On the sides AB, BC and AC of the triangle ABC points P, M and K are chosen so that the segments AM, BK and CP intersect at one point and AM+BK+CP=0 Prove that P, M and K are the midpoints of the sides of the triangle ABC.