RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 15 of Formative Assessment (Unit Test)

Listen NCERT Audio Books to boost your productivity and retention power by 2X.


Prove that the parallelogram circumscribing a circle, is a rhombus.

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

To Proof : ABCD is a rhombus.

As ABCD is a parallelogram

AB = CD and BC = AD …[1]

[opposite sides of a parallelogram are equal]

Now, As tangents drawn from an external point are equal.

We have


[tangents from point A]


[tangents from point B]


[tangents from point C]


[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, ABCD is a rhombus.

Hence Proved.

Chapter Exercises

More Exercise Questions