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Q.

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?


Question Image

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a

18 cm

b

27 cm

c

36 cm

d

32 cm 

answer is C.

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Detailed Solution

Consider the given figure,
Question ImageGiven that, AP=6cm,   BP=5cm,   CQ=3cm,   and DR=4cm   .
We know that tangents drawn from external points to a circle are equal.
Question ImageCalculating AB,
Question ImageCalculating BC,
Question ImageCalculating CD,
CD=CR+RD ⇒CD=3+4 ⇒CD=7cm  
Calculating AD,
Question ImageThen, 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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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?