Question

Using distance formula, show that (3,3) is the centre of the circle passing through the points (6,2) ,(0,4) and (4,6)

Answer 1

If (3,3) is the centre of the three points (6,2) , (0,4) and (4,6), then the distance between (3,3) and these three points will be equal.

distance to (6,2) := root((6-3)^2 + (2-3)^2)
= root(9 + 1)
= root(10)

distance to (0,4) : = root((0-3)^2 + (4-3)^2)
= root(9 + 1)
= root(10)

distance to (4,6) : = root((4-3)^2 + (6-3)^2)
= root(1 + 9)
= root(10)

Hence, proved.