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Question

If orthocentre and circumcentre of a triangle are respectively $$(1, 1)$$ and $$(3, 2)$$, then the coordinates of its centroid are:


A
(73,53)
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B
(53,73)
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C
(7,5)
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D
none of these
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Solution

The correct option is A $$\left( \dfrac { 7 }{ 3 } ,\dfrac { 5 }{ 3 } \right) $$
We know that in a traingle the centroid divides the line joining the orthocentre and circumcentre in the ratio $$2:1$$,
$$\therefore$$ centroid is $$\left( \dfrac { 2(3)+1 }{ 2+1 } ,\dfrac { 2(2)+1 }{ 2+1 }  \right) \\ \Longrightarrow \left( \dfrac { 7 }{ 3 } ,\dfrac { 5 }{ 3 }  \right) $$

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