2

Part of 1990 Kurschak Competition

Problems(1)

A concurrency with excenters

Source: Kürschák 1990, problem 2

The incenter of

J_i

I

, and the center of the

A_i

J_i

i=1,2,3

B_i

be the intersection point of side

A_{i+1}A_{i+2}

and the bisector of

\angle A_{i+1}IA_{i+2}

A_{i+3}:=A_i

\forall i

). Prove that the three lines

B_iJ_i

are concurrent.

geometryincentertrigonometryratioangle bisectortrig identitiesLaw of Sines