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perpendicular segments

Source: Balkan MO 2014 G-5

June 10, 2015

geometrytrapezoid

Problem Statement

Let

ABCD

be a trapezium inscribed in a circle

k

with diameter

K

. A circle with center

B

and radius

BE

,where

E

is the intersection point of the diagonals

AC

and

BD

meets

k

at points

K

and

L

. If the line ,perpendicular to

BD

at

E

,intersects

CD

at

M

,prove that

KM\perp DL

.

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