Question

if all the sides of a parallelogram touch a circle show that parallelogram is a rhombus

Answer 1

it would be the answer

Answer 2

From A, AP and AS are tangents to the circle.

Therefore, AP = AS.......(i)

Similarly, we can prove that:

BP = BQ .........(ii)

CR = CQ .........(iii)

DR = DS .........(iv)

Adding,

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

AB + CD = AD + BC

Hence, AB + CD = AD + BC

But AB = CD and BC = AD.......(v) Opposite sides of a ||gm

Therefore, AB + AB = BC + BC 2AB = 2 BC AB = BC ........(vi)

From (v) and (vi)

AB = BC = CD = DA

Hence, ABCD is a rhombus