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In the given figure, quadrilateral ABCD is circumscribed, touching the circle at P,Q,R and S. If AP=6 cm, BP=5 cm, CQ=3 cm and DR=4 cm then, which of the following is the perimeter of quadrilateral ABCD?

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18 cm

27 cm

36 cm

32 cm

answer is C.

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Detailed Solution

Consider the given figure,
Question Image

Given that,

A P = 6 c m,

B P = 5 c m,

C Q = 3 cm,

and

D R = 4 cm

.
We know that tangents drawn from external points to a circle are equal.

Calculating AB,
Question Image

Calculating BC,
Question Image

Calculating CD,

C D = C R + R D ⇒ C D = 3 + 4 ⇒ C D = 7 c m

Calculating AD,
Question Image

Then, the perimeter of quadrilateral ABCD is,
Question Image

Hence, the perimeter of quadrilateral ABCD is 36cm.
Therefore, option 3 is correct.

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