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Question
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
Solution
Given, the points A(4,3) and B(x,5) lie on a circle with center o(2,3) . Then OA = OB
Also `(OA)^2 = (OB)^2`
`⇒(4-2)^2 + (3-3)^2 = (x-2) ^2 +(5-3)^2`
`⇒(2)^2+(0)^2=(x-2)^2 +(2)^2`
`⇒ 4=(x-2)^2 +4`
`⇒(x-2)^2 =0`
⇒ x -2 = 0
⇒ x =2
Therefore, x= 2
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