Question

State True or False.

The parallelogram circumscribing a circle is a rhombus.

• A. 5cm
• B. False

Answer 1

The correct option is A

5cm

A parallelogram ABCD circumscribes a circle with centre O.

We know that the lengths of tangents drawn from an exterior point to a circle are equal.

$\therefore$ AP = AS, . . . (i) [tangents from A]

BP = BQ, . . . (ii) [tangents from B]

CR = CQ, . . . (iii) [tangents from C]

DR = DS . . . (iv) [tangents from D]

Adding (i), (ii), (iii) and (iv), we get,

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

AB + CD = AD + BC . . . (v)

But we know that in a parallelogram opposite sides are equal.

$\therefore$ AD = BC and AB = CD, putting these in (v) we get

2 AB = 2 AD

AB = AD = CD = BC.

Hence, ABCD is a rhombus.