feet of perpendicular and midpoint

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RJHridi
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feet of perpendicular and midpoint

Unread post by RJHridi » Mon Apr 04, 2016 2:02 pm

In any triangle ABC, P, Q, R are the feet of perpendiculars from a point S to the sides BC, CA, AB respectively. L, M, N, are the midpoints of these sides. Prove that (LP)(BC) + (MQ)(CA) + (NR)(AB) = 0
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asif e elahi
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Location:Sylhet,Bangladesh

Re: feet of perpendicular and midpoint

Unread post by asif e elahi » Wed Apr 27, 2016 4:17 pm

It will be equal to $0$ if you take directed segment, otherwise not.

Hint
Write $\vec{LP}.\vec{BC}$ in terms of $\vec{BP}$ and$\vec{CP}$.
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