Question 54
Consider a triangle $ABC$ with $AC \gt AB$ and $\angle ACB = 60^\circ$. Let $D$ be a point on side $BC$ such that $AD$ is the angle bisector of $\angle BAC$ and $AB = AD$. Point $E$ lies on line $AD$ such that $D$ is between $A$ and $E$, and $AE = AC$. Point $F$ lies on line $AB$ such that $B$ is between $A$ and $F$. Point $T$ is on segment $AE$ such that $BF = TE = CD$. Show that:
a) $EF = CT$;
b) $AC = BC + BT$.
a) $EF = CT$;
b) $AC = BC + BT$.