Question 44
Construct outside the square $ABCD$ the right isosceles triangle $ABE$, with hypotenuse $[AB]$. Denote $N$ the midpoint of the segment $[AD]$ and $\{M\} = CE \cap AB$, $\{P\} = CN \cap AB$, $\{F\} = PE \cap MN$. Take on the straight line $FP$ the point $Q$ so that $[CE$ is the bisector of the angle $\angle QCB$. Prove that $MQ \perp CF$.
Sorin Furtună
Sorin Furtună