Question 3

# If the co-ordinates of orthocentre and the centroid of a triangle ABC are (—5, 7) and (5, 5), then the circumcentre of the triangle ABC is :

Solution

Centroid divides orthocenter and circumcenter in the ratio of 2:1

The co-ordinates of orthocentre and the centroid of a triangle ABC are (—5, 7) and (5, 5)

Let the co-ordinate of circumcenter be (x,y)

5=$$\ \frac{\ 2x-5}{3}\ =\ 5$$ and $$\ \frac{\ 2y+7}{3}\ =\ 5$$

x=10 and y = 4

Hence the circumcenter = (10, 4)