MathDB

Execenter and incircle problem

Source: Russian TST 2014, Day 9 P1 (Groups A & B)

January 8, 2024

geometryincircle

Problem Statement

The inscribed circle of the triangle

ABC{}

touches the sides

BC,CA

and

AB{}

A',B'

and

C'{}

respectively. Let

I_a

be the

A

-excenter of

ABC{}.

Prove that

I_aA'

is perpendicular to the line determined by the circumcenters of

I_aBC'

and

I_aCB'.