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determine the ratio

Source: Netherlands 1993

June 28, 2009

ratiogeometry proposedgeometry

Problem Statement

In a triangle

ABC

with \angle A\equal{}90^{\circ},

D

is the midpoint of

BC

,

F

that of

AB

,

E

that of

AF

and

G

that of

FB

. Segment

AD

intersects

CE,CF

and

CG

in

P,Q

and

R

, respectively. Determine the ratio:

\frac{PQ}{QR}

.

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