# If orthocentre and circumcentre  of a $\bigtriangleup$ are respectively (1,1) and (3,2) , then the coordinates of its  centroid  are  Option 1) $\left ( \frac{7}{5},\frac{5}{3} \right )$ Option 2) $\left ( \frac{5}{3},\frac{7}{3} \right )$ Option 3) $\left ( 7,5 \right )$ Option 4) None

D Divya Saini

Euler line -

In any non equilateral triangle the circumcentre (O), the centriod (G) and the orthocentre (H) are collinear and G divides OH in ratio 1:2

- wherein

Cr = Centroid; Orthocentre$\equiv H;$ Circumcentre $\equiv 0$

$\frac{GO}{GH}=\frac{1}{2}$                                 $H\equiv (1, 1)$

$O\equiv (3, 2)$

$G\equiv (h, k)$

$\frac{2\times 3+1\times 1}{1+2} = h$

$\Rightarrow h=\frac{7}{3}$

$\frac{1\times 1+2\times 2}{1+2}=k$

$\Rightarrow k=\frac{5}{3}$

Option 1)

$\left ( \frac{7}{5},\frac{5}{3} \right )$

This solution is correct

Option 2)

$\left ( \frac{5}{3},\frac{7}{3} \right )$

This solution is incorrect

Option 3)

$\left ( 7,5 \right )$

This solution is incorrect

Option 4)

None

This solution is incorrect

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