MathDB
Easy Geometry with Simple Property about OI Line

Source: 2020 Taiwan TST Round 2 Mock Exam P6

April 24, 2020
geometrygeometry proposed

Problem Statement

Let I,O,ω,ΩI, O, \omega, \Omega be the incenter, circumcenter, the incircle, and the circumcircle, respectively, of a scalene triangle ABCABC. The incircle ω\omega is tangent to side BCBC at point DD. Let SS be the point on the circumcircle Ω\Omega such that AS,OI,BCAS, OI, BC are concurrent. Let HH be the orthocenter of triangle BICBIC. Point TT lies on Ω\Omega such that ∠ATI\angle ATI is a right angle. Prove that the points D,T,H,SD, T, H, S are concyclic.
Proposed by ltf0501
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