Q. 545.0( 1 Vote )

# Assertion - and - Reason TypeEach question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following codeA. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A)B. Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).C. Assertion (A) is true and Reason (R) is false.D. Assertion (A) is false and Reason (R) is true.

Let PT and PQ are two tangents from external point P to a circle with center O

In OPT and OQT

OP = OQ

OT = OT

[common]

PT = PQ

[Tangents drawn from an external point are equal]

OPT OQT

[By Side - Side - Side Criterion]

POT = QOT

[Corresponding parts of congruent triangles are congruent]

i.e. Assertion is true

Now,

Consider a circle circumscribed by a parallelogram ABCD, Let side AB, BC, CD and AD touch circles at P, Q, R and S respectively.

As ABCD is a parallelogram

AB = CD and BC = AD

[opposite sides of a parallelogram are equal] [1]

Now, 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

AB + AB = BC + BC [From 1]

AB = BC …[2]

From [1] and [2]

AB = BC = CD = AD

And we know,

A parallelogram with all sides equal is a rhombus

So, reason is also true, but not a correct reason for assertion.

Hence, B is correct option .

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