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  • Write ‘True’ or ‘False’ and justify your answer in each of the following If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.

Write ‘True’ or ‘False’ and justify your answer in each of the following: If several circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.

Answers (1)

 According to the question.

Here C1, C2, C3 are the circle with center O1, O2, O3 respectively.
C1, C2, C3 touches line PQ at point A. Here PQ is the tangent at each circle.
If we join O1, O2, and O3 to point A then the line is perpendicular to line PQ because if we draw a line from the centre of the circle at any point then the tangent at that point is perpendicular to the radius.
But here line joining the centres is not bisecting the line PQ because it depends on the length of PQ.
Hence the given statement is False.

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infoexpert27

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