The line ax + by + c = 0 is a normal to the c | vedclass

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(C) line is a normal to a circle if and only if it passes through the center of the circle.The center of the circle $x^2 + y^2 = r^2$ is $(0, 0)$.Sinc

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$2r$

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(C) line is a normal to a circle if and only if it passes through the center of the circle.The center of the circle $x^2 + y^2 = r^2$ is $(0, 0)$.Since the line $ax + by + c = 0$ is a normal,it must pass through $(0, 0)$,which implies $c = 0$.The line passes through the center,so it is a diameter of the circle.The length of the chord formed by a diameter is equal to the diameter of the circle.The diameter of the circle is $2r$.Therefore,the length of the intercept is $2r$.

The line $ax + by + c = 0$ is a normal to the circle $x^2 + y^2 = r^2$. The length of the intercept made by the circle on the line $ax + by + c = 0$ is:

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