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.

HINT: OA² = OB².

Answer 1

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