Question 2
Let $ABCD$ be an isosceles trapezoid with $CD$ its larger base. A point $M$ moves on the line $CD$, distinct from $C,D$. Let $N$ be the second intersection, other than $M$, of circles $(BCM)$ and $(DAM)$. Prove that:
1. $N$ moves on a fixed circle.
2. The line $MN$ always passes through a fixed point.
Here $(XYZ)$ denotes the circle through $X,Y,Z$.
1. $N$ moves on a fixed circle.
2. The line $MN$ always passes through a fixed point.
Here $(XYZ)$ denotes the circle through $X,Y,Z$.