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Addition of Vectors

If S is the...

Question

If $S$ is the circumcentre, $O$ is the orthocenter of $△ A B C,$ then $S A + S B + S C =$

A

S O

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B

2 S O

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C

O S

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D

2 O S

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Solution

The correct option is A $S O$
From geometry
$2 S D = A O,$ where $D$ is the mid.
Point of $B C .$
$∴ S A + S B + S C = S A + S D + D B + S D + D C$
$= S A + 2 S D$
$= S A + A O = S O$
$∴ S A + S B + S C = S O .$

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