MathNet 2016-part-01 — 184 problems (EN–VI) Question 122

Given the triangle $ABC$ with $AB = 2AC$. If points $M$ and $N$ belong to the sides $BC$ and $AB$, respectively, and the perimeter of the trapezoid $CMNA$ is the sum of the lengths of the sides $AB$ and $AC$, construct $M$ using compasses and ruler.

(S. Mazanik)