Question 46
Given a circle $(O)$ with diameter $AB$ on the plane. A point $P$ moves on the tangent at $B$ to $(O)$. The line $PA$ intersects $(O)$ in the second point $C$. Let $D$ be the point symmetric to $C$ with respect to $O$. The line $PD$ intersects $(O)$ in the second point $E$.
1/ Show that the lines $AE$, $BC$ and $PO$ pass through a common point. Call this point $M$.
2/ Determine the place of $P$ such that the triangle $ABC$ has maximum area. Compute that maximum area in terms of the radius of $(O)$.
1/ Show that the lines $AE$, $BC$ and $PO$ pass through a common point. Call this point $M$.
2/ Determine the place of $P$ such that the triangle $ABC$ has maximum area. Compute that maximum area in terms of the radius of $(O)$.