Question 30
Let $ABC$ be a triangle with $\angle BAC = 40^\circ$ and $\angle ABC = 60^\circ$. Let $D$ and $E$ be the points lying on the sides $AC$ and $AB$, respectively, such that $\angle CBD = 40^\circ$ and $\angle BCE = 70^\circ$. Let $F$ be the point of intersection of the lines $BD$ and $CE$. Show that the line $AF$ is perpendicular to the line $BC$.