MathNet 2016-part-04 — 184 problems (EN–VI) Question 97

In triangle $ABC$, the measures of the angles $B$ and $A$ are directly proportional to $2$ and $3$. Take $M$ and $N$ on the sides $[AB]$ and $[BC]$ respectively, so that $BN = NM = MC = MA$. Prove that:

a) one of the obtained triangles is equilateral;

b) $CM \perp AB$.