If the points A(4,3) and B(x,5) are on the circle with centre O(2,3) find the value of x.
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Given O (2,3) is the center of the circle .
(Diagram in attachment)
Given points are A(4,3) and B(x,5)
Using distance formula,
√(2-4)^2 + (3-3)^2 = √(x-2)^2 + (5-3)^2
√(-2)^2 + (0) = √ x^2 - 4x + 4 + (2)^2
√4 = √x^2 - 4x +4 + 4
Squaring both sides,
4 = x^2 - 4x + 8
x^2 - 4x + 8 - 4 = 0
x^2 - 4x + 4 = 0
x^2 - 2x - 2x + 4 = 0
x( x - 2 ) - 2( x - 2 ) = 0
( x - 2 ) ( x - 2) = 0
x - 2 = 0
x = 2
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