Question 35
We consider a triangle $ABC$ and a point $D$ on the extended line segment $AB$ on the side of $B$. The point $E$ lies on side $AC$ such that the angles $\angle DBC$ and $\angle DEC$ are equal. The intersection of $DE$ and $BC$ is $F$. Suppose that $|BF| = 2$, $|BD| = 3$, $|AE| = 4$, and $|AB| = 5$. (Attention: the picture has not been drawn to scale.)
a.
Prove that triangles $\triangle ABC$ and $\triangle AED$ are similar.
b.
Determine $|CF|$.
a.
Prove that triangles $\triangle ABC$ and $\triangle AED$ are similar.
b.
Determine $|CF|$.