Given a quadrilateral ABCD, inscribed in a circle ω such that AB=AD and CB=CD . Take the point P∈ω. Let the vertices of the quadrilateral Q1Q2Q3Q4 be symmetric to the point P wrt the lines AB, BC, CD, and DA, respectively.
a) Prove that the points symmetric to the point P wrt lines Q1Q22,Q2Q3,Q3Q4 and Q4Q1, lie on one line.
b) Prove that when the point P moves in a circle ω, then all such lines pass through one common point. geometryconcurrencyConcyclicsymmetrycyclic quadrilateralUkrainian TYM