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.

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AO = OB (BOTH are radii of the same circle)

AO = root of (2-4)2 + (3-3)2

 = root (-2)2 = root 4 = 2

BO = root (2-x)2 + (3-5)2

  = root x2 - 4x + 4 + (-2)2

 = root x2 - 4x + 4  + 4

= root x2 - 4x + 8

As AO = BO

=> ROOT x2 - 4x + 8 = 2

squaring booth sides

 x2 - 4x + 8  = 4

=x2 - 4x + 8 - 4 = 0

x2 - 4x + 4 = 0

x2 - 2x - 2x + 4 = 0

x(x-2)  -2  (x-2) =0

(x-2) (x-2) =0

x= 2, 2 0r x = 2

 

hope you understand... best of luck

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