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.

Answer :


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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