MathDB
Mixtilinear circle property

Source: 2018 Korea Winter Program Practice Test #5

January 7, 2018
mixtilinear incirclegeometrycircumcircle

Problem Statement

Let ΔABC\Delta ABC be a triangle with circumcenter OO and circumcircle ww. Let SS be the center of the circle which is tangent with ABAB, ACAC, and ww (in the inside), and let the circle meet ww at point KK. Let the circle with diameter ASAS meet ww at TT. If MM is the midpoint of BCBC, show that K,T,M,OK,T,M,O are concyclic.
Back to ProblemsView on AoPS