Q1 of 59 Page 83

Four alternative answers for each of the following questions are given. Choose the correct alternative.

A circle touches all sides of a parallelogram. So the parallelogram must be a,................... .



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.

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