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Position of a Line with Respect to Circle

The line ax...

Question

The line $a x + b y + c = 0$ is normal to the circle $x^{2} + y^{2} = r^{2}$ . The portion of the line $a x + b y + c = 0$ intercepted by this circle is of length

A

r

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B

r^{2}

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C

2 r

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D

\sqrt{r}

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Solution

The correct option is C $2 r$
Normal to a circle always passes through the center of circle
It is the diameter of circle so
The length of diameter is $2 r$

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x^{2} + y^{2} = 25.

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x^{2} + y^{2} = 25.

The portion of the line

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A x + B y + C = 0

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