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

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)

⇒ $O{B}^2=O{A}^2$

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

⇒ $(x–2{)}^2+4=4$

⇒ $(x–2{)}^2=0$

⇒ x – 2 = 0

⇒ x = 2

Thus, the value of x is 2.