13

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

Two lines concur on (ABC)

Source: XVII Sharygin Corespondnce Round P13

ABC

with circumcircle

\Omega

I

M

BAC

\overline{AI}

\Omega

N\ne A

. The excircle opposite to

A

\overline{BC}

E

Q\ne I

on the circumcircle of

\triangle MIN

\overline{QI}\parallel\overline{BC}

. Prove that the lines

\overline{AE}

\overline{QN}

\Omega

geometryexcircleincentermixtilinearconcurrencySharygin Geometry Olympiadanant mudgal geo