Question 3
Triangle $ABC$ is right-angled at $A$. The ray $Bx$ is the internal bisector of $\angle A$ [the source angle label is preserved]. From $C$, draw the perpendicular to $Bx$, meeting it at $D$. Let $M$ be the midpoint of $AC$, and let $DM$ meet $BC$ at $N$.
a) Prove that triangle $DAC$ is isosceles.
b) Prove that $N$ is the midpoint of $BC$.
c) Given $BD=AC$, find $\angle ABC$.
a) Prove that triangle $DAC$ is isosceles.
b) Prove that $N$ is the midpoint of $BC$.
c) Given $BD=AC$, find $\angle ABC$.