Q.

In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P,Q,R and S respectively. If the radius of the circle is 10 cm, BC=38 cm, PB=27 cm and AD CD, then which of the following is the length of CD?


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a

11 cm

b

15 cm

c

20 cm

d

21 cm 

answer is D.

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Detailed Solution

Consider the given figure,
Question ImageGiven that,
OS= OR= 10 cm, BC=38 cm, PB=27 cm and AD CD.
We know that tangent segments to a circle from the same external point are congruent, so, BP=BQ  
BQ=27cm   and CQ=CR   .
Therefore,
Question ImageAll the angles in quadrilateral DROS are right angles. Therefore, DROS is a rectangle.
We know that opposite sides of the rectangle are equal.
Therefore, OS=RD   i.e., RD=10cm  .
Then, the value of CD is,
Question ImageHence, the length of CD is 21cm   .
Therefore, option 4 is correct.
 
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