Question

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

Answer 1

The given points A(4, 3) and B(x, 5) lie on the circle with centre 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