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)
⇒ OB2 = OA2
⇒ (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.