## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 55 of Multiple Choice Questions (MCQ)

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55
##### Assertion - and - Reason TypeEach question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

For Assertion :

In the given Figure,

As tangents drawn from an external point are equal.

We have

AP = AS

[tangents from point A]

BP = BQ

[tangents from point B]

CR = CQ

[tangents from point C]

DR = DS

[tangents from point D]

AP + BP + CR + DR = AS + BQ + CQ + DS

AB + CD = AS + DS + BQ + CQ

AB + CD = AD + BC

So, assertion is not true

For Reason,

Consider two concentric circles with common center O and AB is a chord to outer circle and is tangent to inner circle P.

Now,

OP AB

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

We know, that perpendicular from center to chord bisects the chord.

So, P bisects AB.

Reason is true

Hence, Assertion is false, But Reason is true.

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