Question 130
Let $\triangle ABC$ be a triangle with $\angle BAC = 30^\circ$ and $\angle ABC = 100^\circ$. Let $m$ be the perpendicular bisector of $AC$, $E$ be the intersection of $m$ and $AB$, and $D$ be the point on $m$, inside the triangle $ABC$, such that $\angle CAD = 10^\circ$. Let $M$ be the intersection of the lines $AD$ and $CE$.
a) Prove that $CE$ is the bisector of the angle $\angle BCD$.
b) Prove that $AM = AB$.
a) Prove that $CE$ is the bisector of the angle $\angle BCD$.
b) Prove that $AM = AB$.