Question

Parallelogram touch an inner circel

Answer 1

Let ABCD be a parallelogram which circumscribes the circle.

AP = AS [Tangents drawn from an external point to a circle are equal in length]

BP = BQ [Tangents drawn from an external point to a circle are equal in length]

CR = CQ [Tangents drawn from an external point to a circle are equal in length]

DR = DS [Tangents drawn from an external point to a circle are equal in length]

Consider, (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)

AB + CD = AD + BC

But AB = CD and BC = AD  [Opposite sides of parallelogram ABCD]

AB + CD = AD + BC

Hence 2AB = 2BC

Therefore, AB = BC  

Similarly, we get AB = DA and  DA = CD

Thus, ABCD is a rhombus.

Answer 2

Here is your answer:-

》》Parallelogram touchs an inner circle that is parallelogram inscribes the circle.

》》Thus it becomes rhombus..

Here is an image of it in given attachment.

Hope you understand...☆☆