All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?

15 cm

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34 cm

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20 cm

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80 cm

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Solution

The correct option is B
34 cm

If two tangents are drawn to a circle from an exterior point, then the tangents are equal in length.

Hence, in the above figure,
BQ = PB = 4 cm (tangents from an exterior point are equal in length)
Similarly, QC = CR = 6 cm
RD = SD = 3 cm
AS = AP = 4 cm

$∴$ Perimeter of the quadrilateral ABCD
= BC + CD + DA + AB
= 10 + 9 + 7 + 8
= 19 + 15 = 34 cm

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