MathNet 2024-part-01 — 168 problems (EN–VI) Question 84

Given a triangle $ABC$ and $M$, the midpoint of $AB$. It is given that $\angle ABC = 30^\circ$ and $\angle BCM = 105^\circ$. Prove that $CM \cdot AC = BM \cdot BC$.
(Konstantin Delchev)