Prove that abcd>=3

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Nice problem (Triangle)

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Jacobi’s theorem (Geometry)

Jacobi's theorem
http://www.gogeometry.com/geometry/isogonic_jacobi_theorem.htm

Find [PQR]/[ABC]=?

Let P, Q, R be points on the sides BC, CA, AB of triangle \Delta ABC. Let QR cut AP at O. Letet \displaystyle x=\frac{BR}{RA}, y=\frac{CQ}{QA}, k=\frac{PO}{OA}.
Prove that \displaystyle \frac{[PQR]}{[ABC]}=\frac{k}{(1+x)(1+y)}
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Miguel equaltion

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van khea’s problem

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van khea problem

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