MathDB

Incenters on an inscribed quadrilateral

Source: 2023 Turkey Junior National Olympiad P2

December 22, 2023

geometryincenter

Problem Statement

Let

ABCD

be an inscribed quadrilateral. Let the incenters of

BAD

and

CAD

I

and

J

respectively. Let the intersection point of the line that passes through

I

and perpendicular to

BD

and the line that passes through

J

and perpendicular to

AC

K

. Prove that

KI=KJ