Find the circumcentre of a triangle with vert | vedclass

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(D) The given vertices are $A(8,6)$,$B(8,-2)$,and $C(2,-2)$.First,observe the nature of the triangle. The side $AB$ is vertical (constant $x=8$) and t

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$(5,2)$

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(D) The given vertices are $A(8,6)$,$B(8,-2)$,and $C(2,-2)$.First,observe the nature of the triangle. The side $AB$ is vertical (constant $x=8$) and the side $BC$ is horizontal (constant $y=-2$).Since $AB$ is perpendicular to $BC$,the triangle $ABC$ is a right-angled triangle with the right angle at vertex $B(8,-2)$.In a right-angled triangle,the circumcentre is the midpoint of the hypotenuse.The hypotenuse is the side $AC$ connecting vertices $A(8,6)$ and $C(2,-2)$.The midpoint of $AC$ is calculated as $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) = (\frac{8+2}{2}, \frac{6-2}{2}) = (\frac{10}{2}, \frac{4}{2}) = (5,2)$.Thus,the circumcentre is $(5,2)$.

Find the circumcentre of a triangle with vertices $A(8,6)$,$B(8,-2)$,and $C(2,-2)$.

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