The parallelogram circumscribing a circle is a ____.

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The parallelogram circumscribing a circle is a rhombus.
Given that a parallelogram circumscribes a circle with center

O

Assuming that

ABCD

is a parallelogram,

A B = B C = C D = A D

[Given]
Tangents drawn are equal if they are from the same external point, therefore

AP = AS … … (i) BP = BQ … … (ii) CR = CQ … … (iii) DR = DS … … (iv)

Adding

AB

and

CD

AB + CD = AP + BP + CR + DR = AS + BQ + CQ + DS

[From (i), (ii), (iii) and (iv)]

= (AS + DS) + (BQ + CQ) AB + CD = AD + BC

We use the parallelogram property which states that the opposite sides of a parallelogram are equal.

2 AB = 2 AD AB = AD CD = AB = AD = BC

Thus, the parallelogram circumscribing a circle is a rhombus.

Watch 3-min video & get full concept clarity