Given is a triangle ABC and a point K within the triangle. The point K is mirrored in the sides of the triangle: P,Q and R are the mirrorings of K in AB,BC and CA, respectively . M is the center of the circle passing through the vertices of triangle PQR. M is mirrored again in the sides of triangle ABC: P′,Q′ and R′ are the mirror of M in AB respectively, BC and CA.
a. Prove that K is the center of the circle passing through the vertices of triangle P′Q′R′ .
b. Where should you choose K within triangle ABC so that M and K coincide? Prove your answer. geometryCircumcentersymmetry