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

@MeameJohan: Good answer! Keep posting!

Given, A (4, 3) and B (*x*, 5) are two points on the circle. Centre of the circle is O (2, 3).

∴ OB = OA (Radius of the circle)

⇒ OB^{2} = OA^{2}

⇒ (*x* – 2)^{2} + (5 – 3)^{2} = (4 – 2)^{2} + (3 – 3)^{2 } [Distance formula]

⇒ (*x* – 2)^{2} + 4 = 4

⇒ (*x* – 2)^{2} = 0

⇒ *x* – 2 = 0

⇒ *x* = 2

Thus, the value of *x* is 2.

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