Question

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

Answer 1

The answer is given below :

The centre of the circle is at O (2, 3).

The two points A (4, 3) and B (x, 5) lie on the circle.

Then both OA and OB determine the radius of the circle.

Hence, length of OA = length of OB

$= > \sqrt{ {(4 - 2)}^{2} + {(3 - 3)}^{2} } = \sqrt{ {(x - 2)}^{2} + {(5 - 3)}^{2} } \\ \\ = > \sqrt{ {2}^{2} + {0}^{2} } = \sqrt{ {(x - 2)}^{2} + {2}^{2} } \\ \\ = > \sqrt{4} = \sqrt{ {(x - 2)}^{2} + 4} \\ \\ now \: \: squaring \: \: both \: \: sides \: \: we \: \: \\ get \\ \\ 4 = {(x - 2)}^{2} + 4 \\ \\ eliminating \: \: 4 \: \: from \: \: both \: \: sides \\ we \: \: get \\ \\ {(x - 2)}^{2} = 0 \\ which \: \: is \: \: a \: \: quadratic \: \: equation \: \: i n \: \: x \\ \\ thu s\: \: x \: \: has \: \: two \: \: value \\ \\ x = 2 \: \: and \: \: x = 2$

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