MathDB
concyclic wanted, circumcircle, angle bisectors midpoint related

Source: 2019 Indonesia MO Province P2 q5 OSP

December 10, 2020
geometrycircumcircleangle bisectorConcyclic

Problem Statement

Given triangle ABCABC, with AC>BCAC> BC, and the it's circumcircle centered at OO. Let MM be the point on the circumcircle of triangle ABCABC so that CMCM is the bisector of ∠ACB\angle ACB. Let Γ\Gamma be a circle with diameter CMCM. The bisector of BOCBOC and bisector of AOCAOC intersect Γ\Gamma at PP and QQ, respectively. If KK is the midpoint of CMCM, prove that P,Q,O,KP, Q, O, K lie at one point of the circle.
Back to ProblemsView on AoPS