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

Solution:

Consider S₁, S₂, S₃, …., S_n be n circles with centers C₁, C₂, C₃, …, C_n.

PQ is a common tangent to all the circles at point A that is common to all circles.

We know that, tangent at any point on the circle is perpendicular to the radius through point of contact

We have,

C₁A ⏊ PQ

C₂A ⏊ PQ

C₃A ⏊ PQ

C_nA ⏊ PQ

Here, C₁ C₂ C₃ … C_n lie on the perpendicular line to PQ but not on the perpendicular bisector as PA may or may not be equal to AQ.

Therefore, the statement is false.

✦ Try This: In the diagram, PQ and PS are two straight lines. Which line is the locus of a point such that it is equidistant from lines PQ and PS?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10

NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 8

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

Summary:

The statement “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” is false

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