Question 65
Let $ABC$ be a triangle such that $\widehat{CAB} \lt \widehat{ABC} \lt \widehat{BCA} \lt 90^{\circ}$. Let $\omega$ be the circumcircle of $ABC$, $\gamma_{a}$ the circle with centre $A$ and radius $AC$, and $\gamma_{b}$ the circle with centre $B$ and radius $BC$. Finally, let $D$ be the intersection point, other than $C$, of $\omega$ and $\gamma_{b}$, and let $E$ be the intersection point, other than $C$, of $\gamma_{a}$ and $\gamma_{b}$.
Prove that the points $A$, $D$ and $E$ are collinear.
Prove that the points $A$, $D$ and $E$ are collinear.