MathDB

DM and BL are parallel

Source: MEMO 2009, problem 6, team competition

October 1, 2009

geometryincenternumber theorygreatest common divisorcyclic quadrilateralgeometry proposed

Problem Statement

Suppose that

ABCD

is a cyclic quadrilateral and CD\equal{}DA. Points

E

and

F

belong to the segments

AB

and

BC

respectively, and \angle ADC\equal{}2\angle EDF. Segments

DK

and

DM

are height and median of triangle

DEF

, respectively.

L

is the point symmetric to

K

with respect to

M

. Prove that the lines

DM

and

BL

are parallel.