MathDB
Yet Another Beautiful OI Geometry Problem

Source: 2021 Taiwan TST Round 1 Independent Study 2-G

March 18, 2021
geometryincentercircumcircle

Problem Statement

Let ABCABC be a triangle with incenter II and circumcircle Ω\Omega. A point XX on Ω\Omega which is different from AA satisfies AI=XIAI=XI. The incircle touches ACAC and ABAB at E,FE, F, respectively. Let Ma,Mb,McM_a, M_b, M_c be the midpoints of sides BC,CA,ABBC, CA, AB, respectively. Let TT be the intersection of the lines MbFM_bF and McEM_cE. Suppose that ATAT intersects Ω\Omega again at a point SS.
Prove that X,Ma,S,TX, M_a, S, T are concyclic.
Proposed by ltf0501 and Li4
Back to ProblemsView on AoPS