Question 15
Let $ABC$ be an isosceles triangle with $AB = AC$ and $\widehat{BAC} \lt 60^\circ$. Let $D$ be the point on $AC$ such that $\widehat{DBC} = \widehat{BAC}$. Let $E$ be the intersection of the perpendicular bisector of $BD$ with the line through $A$ parallel to $BC$. Let $F$ lie on the line $AC$, on the same side of $C$ as $A$, with $FA$ twice $AC$. Finally, let $r$ be the line through $F$ perpendicular to $AB$, $s$ the line through $E$ perpendicular to $AC$, and $t$ the line $BD$. Prove:
(a) the lines $EB$ and $AC$ are parallel;
(b) the lines $r$, $s$ and $t$ are concurrent.
(a) the lines $EB$ and $AC$ are parallel;
(b) the lines $r$, $s$ and $t$ are concurrent.