Question

Find the coordinates of the circumcentre of the triangle whose vertices are ( 8,6) , (8 , -2 ) and ( 2-2 ) . Also , find its circumradius

Answer 1

let (x, y) is the circumcentre of given points
because distance between circumcentre to circumference is always constant
so,
(x-8)^2+(y-6 )^2=(x-8)^2+(y+2)^2=(x-2)^2+(y+2)^2

(x-8)^2+(y-6)^2=(x-8)^2+(y+2)^2
y^2-12y+36=y^2+4y+4
16y=32
y=2

again ,
(x-8)^2+(y+2)^2=(x-2)^2+(y+2)^2
x^2-16x+64=x^2-4x+4
12x =60
x=5

hence circumcentre is (5,2)
and circumradius =root {3^2+4^2}=5 unit