Q. 545.0( 1 Vote )
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
A. 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
[radii of same circle]
OT = OT
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
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] 
Now, As tangents drawn from an external point are equal.
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 …
From  and 
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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