The points A=B are given on the plane. The point C moves along the plane in such a way that ∠ACB=α , where α is the fixed angle from the interval (0o,180o). The circle inscribed in triangle ABC has center the point I and touches the sides AB,BC,CA at points D,E,F accordingly. Rays AI and BI intersect the line EF at points M and N, respectively. Show that:
a) the segment MN has a constant length,
b) all circles circumscribed around triangle DMN have a common point fixedgeometryFixed pointlengthanglescircumcircle