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Question
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
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Solution
Co-ordinates of A = (0, 2)
Co-ordinates of O = (0, 0)
Co-ordinates of B = (1, 2)
Distance between two points = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
By distance formula,
d(O, A) = `sqrt((0 - 0)^2 + (0 - 2)^2`
= `sqrt((0)^2 + (-2)^2`
= `sqrt(0 + 4)`
= 2 ...(i)
d(O, B) = `sqrt((0 - 1)^2 + (0 - 2)^2`
`sqrt((-1)^2 + (-2)^2`
= `sqrt(1 + 4)`
= `sqrt(5)` ...(ii)
∴ From (i) and (ii),
d(O, B) > d(O, A)
∴ d(O, B) > Radius of circle
∴ Point B(1, 2) does not lie on the circle but lies outside the circle.
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