Question 17
$MAB$ is isosceles at $M$ with $AMB \lt 90 ^{\circ}$. The perpendicular to $MB$ at $B$ meets ray $MA$ at $N$. $C$ lies on $MN$ with $NC = NB$. $a$) Prove $ABC = 45 ^{\circ}$. $b$) The perpendicular to $AM$ at $M$ meets ray $BC$ at $D$. Prove $AD = \sqrt{2} MD$.