Question 54
Let $M$ be the centroid of $\triangle ABC$ with $\measuredangle AMB = 2 \measuredangle ACB$. Prove that:
a) $AB^{4} = AC^{4} + BC^{4} - AC^{2} \cdot BC^{2}$;
b) $\measuredangle ACB \geq 60^{\circ}$.
a) $AB^{4} = AC^{4} + BC^{4} - AC^{2} \cdot BC^{2}$;
b) $\measuredangle ACB \geq 60^{\circ}$.