Consider the triangle ABC with ∠BCA>90∘. The circumcircle Γ of ABC has radius R. There is a point P in the interior of the line segment AB such that PB=PC and the length of PA is R. The perpendicular bisector of PB intersects Γ at the points D and E.Prove P is the incentre of triangle CDE. geometryincenterEGMO 2020EGMO