Question 105
Let $ABC$ be a triangle with $AC \gt AB$. Let $P$ be the intersection of $BC$ and the tangent through $A$ to the circumcircle of triangle $ABC$. Let $Q$ be the point on the line $AC$ such that $AQ = AB$ and $A$ lies between $C$ and $Q$. Let $X$ and $Y$ be the midpoints of $BQ$ and $AP$, respectively. Let $R$ be the point on $AP$ such that $AR = BP$ and $R$ lies between $A$ and $P$. Show that $BR = 2XY$.