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2) A circle touches all sides of a parallelogram. So the parallelogram must be a(A) rectangle(B) rhombus(C) square(D) trapezium |
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Answer» Answer: B)RhombusExplanation: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 = 2BC Therefore, AB= BC Similarly, we get AB= DA and DA = CDThus, ABCD is a rhombus. |
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