# An equilateral triangle

Let $P$ be any point inside of an equilateral triangle $\Delta ABC$. Let $D, E, F$ be the projection from $P$ to $BC, CA, AB$. Let $A', B', C'$ are the projections from $A, B, C$ to the line pass through $P$.

Prove that $PE\times BB'+PF\times CC'=PD\times AA'$

Author: Van Khea, Prey Veng, Cambodia

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