MathDB
Incircle and circumcircle

Source: tst- Greece 2019

September 23, 2019
geometry unsolvedgeometrycircumcircle

Problem Statement

Let a triangle ABCABC inscribed in a circle Γ\Gamma with center OO. Let II the incenter of triangle ABCABC and D,E,FD, E, F the contact points of the incircle with sides BC,AC,ABBC, AC, AB of triangle ABCABC respectively . Let also SS the foot of the perpendicular line from DD to the line EFEF.Prove that line SISI passes from the antidiametric point NN of AA in the circle Γ\Gamma.( ANAN is a diametre of the circle Γ\Gamma).