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MCQ

True or False

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

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#### Solution

This statement is **False**.

**Explanation:**Let the S

_{1}, S

_{2}, S

_{3}, …., Sn be n circles with centers C

_{1}, C

_{2}, C

_{3}, …, 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,

C_{1}A ⏊ PQ

C_{2}A ⏊ PQ

C_{3}A ⏊ PQ

C_{n}A ⏊ PQ

So, C_{1}, C_{2}, C_{3} … 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.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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