Question

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

please I need this answer ​

Answer 1

Refer The Attachment ⬆️

• Value of x is 2.

$\Large{✓}$

Hope It Helps You ✌️

Answer 2

Given that, Point A(4, 3) & B(x, 5) lies on the circle with the centre O(2,3).

Therefore, We can say that Centre O(2, 3) is eqidistant from the point A(4, 3) and B(x, 5).

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$\therefore\sf AO = BO\\\\\\ \longrightarrow\sf (AO)^2 = (BO)^2$

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~As we know that, To find out distance between two points we use Distance Formula :

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$\bf{\dag}\:{\underline{\boxed{\blue{\sf{ \pmb{D = \sqrt{\bigg( \red{x_2 - x_1} \bigg)^2 + \bigg( \red{y_2 - y_1} \bigg)^2}}}}}}}$

$:\implies\sf \sqrt{\bigg(4 - 2\bigg)^2 + \bigg(3 - 3\bigg)^2} = \sqrt{\bigg(x - 2\bigg)^2 + \bigg(5 - 3\bigg)^2}\\\\\\ :\implies\sf \bigg(4 - 2\bigg)^2 + \bigg(3 - 3\bigg)^2 = \bigg(x - 2\bigg)^2 + \bigg(5 - 3\bigg)^2\\\\\\ :\implies\sf\cancel{(2)^2} - 0 = (x - 2)^2 + \cancel{(2)^2}\\\\\\ :\implies\sf \sqrt{(x - 2)^2} = \sqrt{0}\\\\\\ :\implies\sf x - 2 = 0\\\\\\ :\implies{\boxed{\boxed{\frak{ \pmb{\purple{ \quad x = 2 \quad}}}}}}$

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$\therefore\:{\underline{\sf{Hence,\:The\: required\: value\:of\:x\: is \:\pmb{2}.}}}$