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6 points on circle again

Source: 2006 Korea National Olympiad #7

March 18, 2018

geometry

Problem Statement

Points

A,B,C,D,E,F

is on the circle

O.

A line

\ell

is tangent to

O

at

E

is parallel to

AC

and

DE>EF.

Let

P,Q

be the intersection of

\ell

and

BC,CD

,respectively and let

R,S

be the intersection of

\ell

and

CF,DF

,respectively. Show that

PQ=RS

if and only if

QE=ER.

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