MathDB

Let

ABCD

be a parallelogram (non-rectangle) and

\Gamma

is the circumcircle of

\triangle ABD

. The points

E

and

F

are the intersections of the lines

BC

and

DC

with

\Gamma

respectively. Define

P=ED\cap BA

Q=FB\cap DA

and

R=PQ\cap CA

. Prove that

\frac{PR}{RQ}=(\frac{BC}{CD})^2

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