10.5

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

prove that the line PQ bisects AD

Source: Sharygin Finals 2023 10.5

The incircle of a triangle

ABC

BC

C

PQ

be the midpoint of arc

\widehat{BAC}

of the circumcircle, and

P

Q

be the projections of

M

to the external bisectors of angles

B

C

respectively. Prove that the line

PQ

AD

geometrySharygin Geometry OlympiadSharygin 2023