Question 10
(BUL 4) Let $M$ be the point inside the right-angled triangle $ABC$ $(\angle C=90^\circ)$ such that
$$\angle MAB=\angle MBC=\angle MCA=\varphi.$$
Let $\psi$ be the acute angle between the medians of $AC$ and $BC$. Prove that $\frac{\sin(\varphi+\psi)}{\sin(\varphi-\psi)}=5$.
$$\angle MAB=\angle MBC=\angle MCA=\varphi.$$
Let $\psi$ be the acute angle between the medians of $AC$ and $BC$. Prove that $\frac{\sin(\varphi+\psi)}{\sin(\varphi-\psi)}=5$.