Question 20
The triangle $ABC$ is isosceles, with $AB = AC$ and $\angle ABC = 72^\circ$. The point $D$ is taken on the line $BC$, so that $C$ is on the segment $BD$ and $CD = AB$.
a) Prove that $AC$ is the bisector of the angle $\angle BAD$.
b) The point $E$ is taken on the parallel to $AB$ through $D$, on the same side of $BD$ as $A$, so that $DE = DB$. Let $F$ be the common point of the lines $AD$ and $BE$. Prove that the lines $AC$ and $AE$ are perpendicular and $AF = FC = BC$.
a) Prove that $AC$ is the bisector of the angle $\angle BAD$.
b) The point $E$ is taken on the parallel to $AB$ through $D$, on the same side of $BD$ as $A$, so that $DE = DB$. Let $F$ be the common point of the lines $AD$ and $BE$. Prove that the lines $AC$ and $AE$ are perpendicular and $AF = FC = BC$.