Question 47
We consider the isosceles right triangle $ABC$, $m(\hat{A}) = 90^\circ$, and the point $D \in (AB)$ such that $AD = \frac{1}{3}AB$. In the half-plane determined by the line $AB$ and the point $C$, one takes the point $E$ for which $m(\angle BDE) = 60^\circ$ and $m(\angle DBE) = 75^\circ$. The lines $BC$ and $DE$ intersect at the point $G$, and the parallel through the point $G$ to the line $AC$ intersects the line $BE$ at the point $H$.
Prove that the triangle *CEH* is equilateral.
Prove that the triangle *CEH* is equilateral.