Q14 of 157 Page 724

If the points A(4, 3) and B(x, 5) lie on a circle with the centre O(2, 3), find the value of x.

OA = √{(4 – 2)2 + (3 – 3)2}


= √4


= 2


OB = √{(x – 2)2 + 4 }


= √{x2 + 4 – 4x + 4}


√{ 8 + x2 – 4x}


OA2 = OB2


4 = 8 + x2 – 4x


⇒ x2 – 4x + 4 = 0


⇒ x2 – 2x – 2x + 4 = 0


⇒ x(x– 2) – 2(x – 2) = 0


⇒ (x – 2) (x – 2) = 0


x = 2


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