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Question 9
If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.

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Solution

True

We drew two circles with centres C1 and C2 passing through the end points P and Q of a line segment PQ.
We know, that perpendicular bisector of a chord of a circle always, passes through the centre of the circle.
Thus, the perpendicular bisector of PQ passes through C1 and C2.
Similarly, all the circle passing through PQ will have their centre on perpendicular bisectors of PQ.

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