Question

Can someone solve this please​

Answer 1

$\large\text{\underline{Let's begin.}}$

The triangle has three vertices:-

$\red{\bigstar A(8,6)}$

$\red{\bigstar B(8,-2)}$

$\red{\bigstar C(2,-2)}$

The triangle is a right triangle since two pairs of vertices are common. $(\overline{AB}\perp\overline{BC})$

$\large\text{\underline{Solution}}$

The circumcentre lies at the midpoint of the hypotenuse.

The points $(2,-2)$ and $(8,6)$ are the hypotenuse of the triangle since no vertice is common.

To find the midpoint of $(2,-2)$ and $(8,6)$,

$\implies(\dfrac{2+8}{2},\dfrac{-2+6}{2})$

$\implies(5,2)$

This is the circumcentre.

$\large\text{\underline{Conclusion}}$

Hence, the co-ordinate of the circumcentre is $(5,2)$.

$\large\text{\underline{Verification}}$

Please view the attachment.