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If the points A(4, 3) and B(x, 5) lie on the circle with centr

Question

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

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Lucas Discussed

If the points

A (4, 3)

and

B (x, 5)

lie on the circle with centre

O (2, 3)

, find the value of x.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Points

A (4, 3)

and

B (x, 5)

lie on the circle with centre

O (2, 3)

Which means:

O A = OB

\Rightarrow O A^{2} = O B^{2}

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

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

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

\Rightarrow 2 - x = 0

x = 2

The value of x is

2

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Question Text	If the points $A (4, 3)$ and $B (x, 5)$ lie on the circle with centre $O (2, 3)$ , find the value of x.
Answer Type	Text solution:1
Upvotes	150