A trapezium PQRS inscribes a circle which touches the circle at M, A, N, B, Radius of the circle is 10 cm. The length of each non-parallel side is 21 cm. What is the perimeter of trapezium?

82 cm

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84 cm

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85.5 cm

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Can't be determined

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Solution

The correct option is B 84 cm
It can be solved using the property of tangents.
(Tangents on the circle drawn from the same points are same in length)
Points M, A, N and B are the points of tangent.
$∴ P S + Q R = P Q + S R = 2 (21) = 42 c m$
$∴$ Perimeter of trapezium = 2(42) = 84 cm

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