MathNet 2017-part-05 — 176 problems (EN–VI) Question 86

Let $ABC$ be a triangle and $D$ the midpoint of the side $BC$. Denote by $E$ the symmetric of $A$ with respect to $D$. Let $F$ be the foot of the perpendicular from $E$ to $AC$. It is known that $AC = 2CF$ and $2m(\angle CAD) + m(\angle BAD) = 90^\circ$. Show that the triangle $ABC$ is equilateral.

Vlad Robu