MathDB

8

Part of 2021 Saudi Arabia Training Tests

Problems(1)

Median IPQ bisects arc BAC

Source: S.A booklet 2021 P8 in problems without solution

9/20/2021
Let ABCABC be an non-isosceles triangle with incenter II, circumcenter OO and a point DD on segment BCBC such that (BID)(BID) cut segments ABAB atE E and (CID)(CID) cuts segment ACAC at FF Circle (DEF)(DEF) cuts segments ABAB,ACAC again at M,NM,N. Let PP The intersection of IBIB and DEDE , QQ The intersection of ICICand DFDF . Prove that EN,FM,PQEN,FM,PQ are parallel and the median of vertex IIin triangle IPQIPQ bisects the arc BACBAC of (O)(O).
geometryIMOgeometry unsolved