Question

give the answer of the question on the pic

Answer 1

Let ABCD be a parallelogram which circumscribes the circle.
AP = AS [Since tangents drawn from an external point to a circle are equal in length]
BP = BQ [Since tangents drawn from an external point to a circle are equal in length]
CR = CQ [Since tangents drawn from an external point to a circle are equal in length]
DR = DS [Since 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  [Since 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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Answer 2

Please refer to this
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