Show that the points (9, -2), (-5, 12) and (-7, 10) lie on that circle whose centre is the point (1, 4)

Explanation

Let the given points are A(9, -2) , B(-5, 12) and C(-7, 10).
If point `O` is (1, 4), then
`" "OA=sqrt((1-9)^(2)+(4+2)^(2))=sqrt((-8)^(2)+(6)^(2))`
` " "=sqrt(64+36)=sqrt(100)=10`
`" "OB =sqrt((1+5)^(2)+(4-12)^(2))=sqrt((6)^(2)+(-8)^(2))`
`" "=sqrt(36+64)=sqrt(100)=10`
and `" "OC=sqrt((1+7)^(2)+( 4-10)^(2))=sqrt((8)^(2)+(-6)^(2))`
` " "=sqrt(64+36)=sqrt(100)=10`
`therefore" "OA=OB=OC`
`rArr` Point 'O' is equidistant from the points A, B and C.
`rArr` Point (1, 4) is the centre of that circle at which the points (9, -2), (-5, 12) and (-7, 10) lie.