Question 41
Let $P$ be a point, inside the triangle $ABC$, so that the triangle $ABP$ is isosceles. On each of the other two sides of $ABC$, triangles $BCQ$ and $CAR$ are constructed externally, both similar to the triangle $ABP$.
Prove that the points $P$, $Q$, $C$ and $R$ are either aligned or are the vertices of a parallelogram.
Prove that the points $P$, $Q$, $C$ and $R$ are either aligned or are the vertices of a parallelogram.