Question 71
Let $ABC$ be a triangle such that $\angle CAB = 30^\circ$ and $\angle ACB = 60^\circ$. An arbitrary point $D$ is chosen on the extension of the ray $AB$ beyond point $B$. The point $E$ lies on the extension of the ray $CB$ beyond the point $B$ such that $\angle BDE = 60^\circ$. The lines $AC$ and $DE$ intersect at $F$.
Prove that the circumcircle of the triangle $AEF$ passes through some fixed point different from $A$ and not depending on the choice of $D$.
(Mikhail Karpuk)
Prove that the circumcircle of the triangle $AEF$ passes through some fixed point different from $A$ and not depending on the choice of $D$.
(Mikhail Karpuk)