Question

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.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

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

C_nA ⏊ PQ

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

PA may or may not be equal to AQ.