Problem

Source: Albanian Mathematical Olympiad 12 GRADE 2011--Question 5

Tags: geometry, circumcircle, analytic geometry, trapezoid, geometry unsolved



The triangle $ABC$ acute with gravity center $M$ is such that $\angle AMB = 2 \angle ACB$. Prove that: (a) $AB^4=AC^4+BC^4-AC^2 \cdot BC^2,$ (b) $\angle ACB \geq 60^o$.