MathNet 2026 — Part 03 Question 104

A triangle is considered $A B C$ with $\angle B A C=45^{\circ}$ and $\angle A C B=30^{\circ}$. If $M$ is the midpoint of the $B C$ side, it is requested to show that $\angle A M B=45^{\circ}$ and $B C \cdot A C=2 \cdot A M \cdot A B$.