## Jacobi’s theorem (Geometry)

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 $\displaystyle \frac{[PQR]}{[ABC]}=\frac{k}{(1+x)(1+y)}$
Propose by Van Khea

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