State true or false.

The parallelogram circumscribing a circle is a rhombus.

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True

False

answer is A.

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Detailed Solution

Suppose ABCD = parallelogram which is circumscribed in a circle. Here opposite side of parallelogram are equal.

\begin{matrix} AB = CD \dots \dots . (1) \\ BC = AD \dots \dots . (2) \end{matrix}

Also,

DR = DS

(From same point D Tangents on circle)
CR = CQ (From same point C Tangents on circle)
BP = BQ (From same point B Tangents on circle)
AP=AS (From same point A Tangents on circle)
Thus,

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

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

CD + AB = AD + BC

2 AB = 2 BC

(from equation 1 and 2)

AB = BC \dots \dots \dots (3)

Thus,

AB = BC = CD = DA

As, all sides of ABCD are equal. Thus, ABCD =Rhombus
Option 1 is correct.

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