Assertion - and - Reason Type

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code

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

In △OPT and △OQT

OP = OQ

[radii of same circle]

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]

Add the above equations

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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