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

Explanation

. Let A(8,6), B(8,-2) and C(2,-2) be the vertices of the given triangle and let P(x,y) be the circumcentre of this triangle. Then

PA=PB=PC

⇒`PA^2=PB^2=PC^2`
⇒`(x−8)^2+(y−6)^2=(x−8)^2+(y+2)^2`

⇒`x^2+y^2−16x−12y+100=x^2+y^2−16x+4y+68`

⇒`16y=32`

⇒`y=2`

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