Question 4
Let $MAB$ be an isosceles triangle with $MA=MB$ and $\angle AMB<90^\circ$. The line perpendicular to $MB$ at $B$ meets ray $MA$ at $N$. Take $C$ on segment $MN$ such that $NC=NB$.
a) Prove that $\angle ABC=45^\circ$.
b) The line perpendicular to $AM$ at $M$ meets ray $BC$ at $D$. Prove that $AD=\sqrt2\,MD$.
a) Prove that $\angle ABC=45^\circ$.
b) The line perpendicular to $AM$ at $M$ meets ray $BC$ at $D$. Prove that $AD=\sqrt2\,MD$.