Let I be the incentre of triangle ABC. A circle containing the points B and C meets the segments BI and CI at points P and Q respectively. It is known that BP⋅CQ=PI⋅QI. Prove that the circumcircle of the triangle PQI is tangent to the circumcircle of ABC.Proposed by S. Berlov geometryincentercircumcircleparallelogrampower of a pointradical axisgeometry proposed