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If all sides of a parallelogram touch a circle then the parallelogram will be a(A) Rectangle(C) Rhombus(B) Square(D) Trapezium |
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Answer» 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 + BCBut AB= CD and BC = AD [Opposite sides of parallelogram ABCD]AB + CD =AD + BCHence 2AB = 2BCTherefore, AB= BC Similarly, we get AB= DA and DA = CDThus, ABCD is a rhombus. |
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