Given an isosceles triangle ABC at A, let M be the midpoint of symmetry of A through C. Let E be the point of symmetry of B through C. On the ray AB take a point N such that B is the midpoint of AN.
a) Prove that quadrilateral BCMN is an isosceles trapezoid
b) Let H and K be the midpoints of AE and NM respectively. Prove that H, C, K are collinear
