Question 21
Outside triangle $ABC$, construct points $X,Y$ such that:
- triangle $AXB$ is isosceles with base $AB$;
- triangle $BYC$ is isosceles with base $BC$;
- $\angle AXB+\angle BYC=180^\circ$.
Let $Z$ be the midpoint of $AC$. Prove that $XZ$ and $YZ$ are perpendicular.
- triangle $AXB$ is isosceles with base $AB$;
- triangle $BYC$ is isosceles with base $BC$;
- $\angle AXB+\angle BYC=180^\circ$.
Let $Z$ be the midpoint of $AC$. Prove that $XZ$ and $YZ$ are perpendicular.