Q. 83.9( 14 Votes )

If a number of circles touch a given line segment PQ at a point A, then their centers lie on the perpendicular bisector of PQ.

Answer :

False


Let the S1, S2, S3, …., Sn be n circles with centers C1, C2, C3, …, Cn respectively.


And The PQ is a common tangent to all the circles at point A which is common to all circles.


As we know,


tangent at any point on the circle is perpendicular to the radius through point of contact


we have,


C1A PQ


C2A PQ


C3A PQ


CnA PQ


So, C1 C2 C3 … Cn all lie on the perpendicular line to PQ but not on perpendicular bisector as


PA may or may not be equal to AQ .


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