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