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Consider triangle $ABC$. Let point $H$ be the orthocentre and point $O$ be the circumcentre.

Prove that area of one of triangles $AOH$,$BOH$,$COH$ is equal to the sum of areas of other two.

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Lee David Chung Lin
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Serik
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    what have you tried so far? Do you have at least drawn a diagram and play around a little with it? – Timbuc Nov 09 '14 at 12:04

1 Answers1

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Hint 1. $\overrightarrow{OH}=\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}$.

Hint 2. Area of $\triangle AOH=\frac12 |\overrightarrow{OA}\times\overrightarrow{OH}|$.

pharmine
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