Question

Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).

Answer 1

Circumcenter of a triangle is the point of intersection of all the three perpendicular bisectors of the sides of triangle. So, the vertices of the triangle lie on the circumference of the circle.

Let the coordinates of the circumcenter of the triangle be (x,y)

Therefore, (x,y) will the equidistant from the vertices of the triangle.

Using distance formula

it is obtained:

As (x,y) is equidistant from all the three vertices

So, D₁=D₂=D₃

D₁=D₂

Adding equations (1) and (2):

⇒x+3y+4x-3y= -6+21

Therefore, 5x=15

⇒ x=15/5

⇒ x=3

When x=3, we get 

Therefore, (3,-3) are the coordinates of the circumcenter of the triangle.