Question 66
Point $X$ is marked inside an acute-angled triangle $ABC$ such that $\angle AXC = \angle A + \angle B$, $\angle BXA = \angle B + \angle C$, $\angle BXC = \angle C + \angle A$.
Prove that $\frac{BC \cdot AX}{AB} = \frac{AB \cdot CX}{AC}$.
Prove that $\frac{BC \cdot AX}{AB} = \frac{AB \cdot CX}{AC}$.