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

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

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If the points

A (4, 3)

and

B (x, 5)

lie on a circle with the centre

O (2, 3)

, find the value of x.

12 mins ago

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12 mins ago

Text solutionVerified

Given: Points

A (4, 3)

and

B (x, 5)

lie on a circle with centre

O (2, 3)

To find: value of x

O A = OB

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

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

O A^{2} = (2 - 4)^{2} + (3 - 3)^{2}

and

O B^{2} = (2 - x)^{2} + (3 - 5)^{2}

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

(- 2)^{2} + 0^{2} = 4 - 4 x + x^{2} + (- 2)^{2}

4 = 4 - 4 x + x^{2} + 4

x^{2} - 4 x + 4 = 0 \Rightarrow (x - 2)^{2} = 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 a circle with the centre $O (2, 3)$ , find the value of x.
Answer Type	Text solution:1
Upvotes	150