Question 180
In triangle $ABC$, the point $D$ lies on segment $AB$ such that $CD$ is the angle bisector of angle $C$. The perpendicular bisector of segment $CD$ intersects the line $AB$ in $E$. Suppose that $|BE| = 4$ and $|AB| = 5$.
a. Prove that $\angle BAC = \angle BCE$.
b. Prove that $2|AD| = |ED|$.
a. Prove that $\angle BAC = \angle BCE$.
b. Prove that $2|AD| = |ED|$.