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Question

If S is circumcenter, G the centroid, O the orthocenter of ABC, then SA+SB+SC is equal to:


A

SG

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B

OS

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C

SO

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D

OG

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Solution

The correct option is C

SO


Explanation for the correct option.

Step 1: Find the centroid

Given, S is the circumcenter, G the centroid, O the orthocenter of ABC.

We solve this by using the concept of vectors.

Let S(0);A;B;C be the vectors of circumcenter.
Then, SA+SB+SC
Centroid G=SA+SB+SC3

Step 2: Find the value of expression
We know the centroid divides the median in 2:1.

HG:GS=2:1
So here G divides HS in 2:1 ratio.
SG=SO+2S3O=3SG=SA+SB+SCSA+SB+SC=SO
Hence, option C is correct.


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