MathDB

Geo quest. [excenters in a parallelogram; < KCL fixed]

Source: IMOTC ST1 Q1; IMO shortlist 2005 problem G3

May 16, 2006

geometryparallelogramhomothetyincenterexterior angleIMO ShortlistSpiral Similarity

Problem Statement

Let

ABCD

be a parallelogram. A variable line

g

through the vertex

A

intersects the rays

BC

and

DC

at the points

X

and

Y

, respectively. Let

K

and

L

be the

A

-excenters of the triangles

ABX

and

ADY

. Show that the angle

\measuredangle KCL

is independent of the line

g

.
Proposed by Vyacheslev Yasinskiy, Ukraine