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Question
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
OA = `sqrt((11 - 1)^2 + (2 - 2)^2`
= `sqrt(10^2 + 0^2)`
= `sqrt(100)`
= 10
OB = `sqrt((11 - 3)^2 + (2 + 4)^2`
= `sqrt(8^2 + 6^2)`
= `sqrt(64 + 36)`
= `sqrt(100)`
= 10
OC = `sqrt((11 - 5)^2 + (2 + 6)^2`
= `sqrt(6^2 + 8^2)`
= `sqrt(36 + 64)`
= `sqrt(100)`
= 10
OA = OB = OC = 10
O is the centre of the circle passing through A, B and C.
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