MathDB

19th kmo #5

Source: KMO round 2, problem 5

February 3, 2006

geometry unsolvedgeometry

Problem Statement

Let

P

be a point that lies outside of circle

O

. A line passes through

P

and meets the circle at

A

and

B

, and another line passes through

P

and meets the circle at

C

and

BC

. The point

A

is between

P

and

B

,

C

is between

P

and

D

. Let the intersection of segment

AD

and

BC

be

L

and construct

E

on ray

(PA

so that

BL \cdot PE = DL \cdot PD

. Show that

M

is the midpoint of the segment

DE

, where

M

is the intersection of lines

PL

and

DE

.

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