MathDB

6

Part of 2018 ITAMO

Problems(1)

Italian MO Problem 6

Source: ITAMO 2018

5/5/2018
Let ABCABC be a triangle with AB=ACAB=AC and let II be its incenter. Let Γ\Gamma be the circumcircle of ABCABC. Lines BIBI and CICI intersect Γ\Gamma in two new points, MM and NN respectively. Let DD be another point on Γ\Gamma lying on arc BCBC not containing AA, and let E,FE,F be the intersections of ADAD with BIBI and CICI, respectively. Let P,QP,Q be the intersections of DMDM with CICI and of DNDN with BIBI respectively.
(i) Prove that D,I,P,QD,I,P,Q lie on the same circle Ω\Omega (ii) Prove that lines CECE and BFBF intersect on Ω\Omega
geometry