State True or False. Given a point $$P$$ inside a circle, different from its centre, there is more than one chord through $$P$$ having $$P$$ as mid point.

Correct Answer: False

Solution

If $$P$$ is the mid point of a chord, the line from the centre $$O$$ to $$P$$ is perpendicular to the chord. Since $$P \ne O$$, the line $$OP$$ is fixed, so there is exactly one line through $$P$$ perpendicular to it. Only one such chord exists, and the statement is False.

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