MathDB

Trapezium inscribed in a circle

Source: Balkan Mathematics Olympiad 2014 - Problem-3

May 4, 2014

geometrytrapezoidtrigonometryincentercircumcircleanalytic geometrypower of a point

Problem Statement

Let

ABCD

be a trapezium inscribed in a circle

\Gamma

with diameter

AB

. Let

E

be the intersection point of the diagonals

AC

and

BD

. The circle with center

B

and radius

BE

meets

\Gamma

at the points

K

and

L

(where

K

is on the same side of

AB

as

C

). The line perpendicular to

BD

at

E

intersects

CD

at

M

. Prove that

KM

is perpendicular to

DL

.
Greece - Silouanos Brazitikos

Back to Problems View on AoPS