Let P be a point in the plane of triangle ABC. Denote the reflections of A,B,C over P by A′,B′ and C′, respectively. Let A′′,B′′,C′′ be the reflection of A′,B′,C′ over BC,CA and AB, respectively. Let the line A′′B′′ intersects AC at Ab and let A′′C′′ intersects AB at Ac. Denote by ωA the circle through the points A,Ab,Ac. The circles ωB,ωC are defined similarly. Prove that ωA,ωB,ωC are coaxial, i.e., they share a common radical axis.Proposed by Navneel Singhal, Delhi and K. V. Sudharshan, Chennai, India power of a pointradical axis