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  • The orthocenter of a triangle lies at the origin and the circumcentre is the midpoint of the segment joining (1, 0) and (2, 3/2). Find the centroid of the triangle<div class='qna-opti

The orthocenter of a triangle lies at the origin and the circumcentre is the midpoint of the segment joining (1, 0) and (2, 3/2). Find the centroid of the triangle

Option: 1

(1, 1)


Option: 2

(1, 1/2)


Option: 3

(1/2, 1/2)


Option: 4

(1, -1/2)


Answers (1)

best_answer

In a triangle, circumcentre, centroid, and orthocentre are collinear and the centroid divides the line joining the circumcentre and orthocentre in the ratio 1:2

Circumcentre (O) = (3/2, 3/4)

Suppose G(x, y) is the Centroid. Then,  OG:GH = 1 : 2

O(3/2, 3/4)------------------------G(x, y)------------------------------------------------H(0,0)

\\\mathrm{x=\frac{2\times \frac{3}{2}++1\times0}{2+1}=1}\\\mathrm{y=\frac{2\times \frac{3}{4}++1\times0}{2+1}=\frac{1}{2}}

Hence, Centroid (G) is (1, 1/2)

Posted by

Irshad Anwar

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