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 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

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] 

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 …

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 .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Quiz | Imp. Qs. on Circle35 mins  Quiz | Imp. Qs. on Circles37 mins  Quiz | Testing Your Knowledge on Circles32 mins  Short Cut Trick to Find Area of Triangle43 mins  Quiz | Areas Related to Circles43 mins  RD Sharma | Area of Sector and Segments25 mins  Quiz | Area Related with Circles47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 