Question 5
Triangle $ABC$ is right-angled at A, with $AB\lt AC$, and M is the midpoint of BC. On the ray opposite to MA, choose D with $MD=MA$. Draw perpendiculars from B and C to AD, meeting it at E and F respectively.
a) Prove that $\angle BFD=\angle CEA$.
b) From D draw the perpendicular to BC, meeting BC at K; let DK meet BE at N. Prove that $AN=NC$.
c) If $\angle ABC=60^\circ$, find $\angle ANC$.
a) Prove that $\angle BFD=\angle CEA$.
b) From D draw the perpendicular to BC, meeting BC at K; let DK meet BE at N. Prove that $AN=NC$.
c) If $\angle ABC=60^\circ$, find $\angle ANC$.