MathDB

An incenter config with a beautiful condition

Source: XVII Sharygin Correspondence Round P17

March 2, 2021

geometryincenter

Problem Statement

Let

ABC

be an acute-angled triangle. Points

A_0

and

C_0

are the midpoints of minor arcs

BC

and

AB

respectively. A circle passing though

A_0

and

C_0

meet

AB

and

BC

at points

P

and

S

Q

and

R

respectively (all these points are distinct). It is known that

PQ\parallel AC

. Prove that

A_0P+C_0S=C_0Q+A_0R