MathDB

Incenters equidistant from midpoint of arc ABC

Source: All-Russian Olympiad 2006 finals, problem 10.6

May 7, 2006

geometryincentercircumcircletrapezoidcomplex numbersgeometry proposed

Problem Statement

Let

K

and

L

be two points on the arcs

AB

and

BC

of the circumcircle of a triangle

ABC

, respectively, such that

KL\parallel AC

. Show that the incenters of triangles

ABK

and

CBL

are equidistant from the midpoint of the arc

ABC

of the circumcircle of triangle

ABC