Question 49
The right isosceles triangle $ABC$ has $m(\angle A) = 90^\circ$. Take $M \in (BC)$ so that $m(\angle AMB) = 75^\circ$ and take $F$ on the internal bisector of the angle $MAC$ so that $BF = AB$. Prove that:
a) the lines $AM$ and $BF$ are perpendicular;
b) the triangle $CFM$ is isosceles.
a) the lines $AM$ and $BF$ are perpendicular;
b) the triangle $CFM$ is isosceles.