Question 161
Let $ABC$ be an isosceles triangle with base $BC$, and let $D, E$ be points on the sides $AB, BC$ respectively, such that the lines $DE$ and $AC$ are parallel. Consider moreover the point $F$ on the line $DE$ which lies on the opposite side of $E$ from $D$ and is such that $FE$ is congruent to $AD$. Letting $O$ be the circumcentre of the triangle $BDE$, prove that the points $O, F, A, D$ lie on a circle.