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

Question:

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

Solution:

Given, the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3).
Then OA = OB
Also (OA)2 = (OB)2

$\Rightarrow(4-2)^{2}+(3-3)^{2}=(x-2)^{2}+(5-3)^{2}$

$\Rightarrow(2)^{2}+(0)^{2}=(x-2)^{2}+(2)^{2}$

$\Rightarrow 4=(x-2)^{2}+4$

$\Rightarrow(x-2)^{2}=0$

$\Rightarrow x-2=0$

$\Rightarrow x=2$

Therefore, x = 2.

 

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Comments

Sakshi
Sept. 20, 2023, 6:35 a.m.
This is very helpful for me. Thank you so much
Nidha
June 21, 2023, 6:35 a.m.
I havva confusion
Ayush Gaur
Feb. 4, 2023, 1:55 p.m.
Not good
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