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

Given: points A (4,3) and B(x,5)

Circle with centre O (2,3)

To find: Value of x.

Formula Used:

The distance between the points (x₁, y₁) and (x₂, y₂) is:

Distance

Explanation:

From the figure, we can see,

OA = OB (radius of circle)

For points A (4,3), B(x,5) and O (2,3).

Taking square on both sides we get,

⇒ 4 = (x – 2)² + 4

⇒ 0 = (x – 2)²

⇒ 0 = (x – 2)

⇒ x = 2

Hence the value of x is 2.