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Question
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
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Solution
The given points A(4, 3) and B(x, 5) lie on the circle with center O(2, 3). Then, OA = OB
`⇒ sqrt((x-2)^2 +(5-3)^2) = sqrt((4-2)^2 +(3-3)^2)`
`⇒ (x-2)^2 +2^2 =2^2+0^2`
`⇒ (x-2)^2 = (2^2 -2^2)`
`⇒ (x-2)^2=0`
⇒ x - 2 = 0
⇒ x = 2
Hence, the value of x = 2
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