MathDB

Simple parallelogram geo

Source: IOM 2017 #1

September 5, 2017

parallelogramgeometryAngle Chase

Problem Statement

Let

ABCD

be a parallelogram in which angle at

B

is obtuse and

AD>AB

. Points

K

and

L

on

AC

such that

\angle ADL=\angle KBA

(the points

ABC

are all different, with

K

between

A

and

L

). The line

BK

intersects the circumcircle

\omega

of

ABC

at points

B

and

E

, and the line

EL

intersects

\omega

at points

E

and

F

. Prove that

BF||AC

.

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