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?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

11 cm

15 cm

20 cm

21 cm

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Consider the given figure,
Question Image

Given 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,

B P = B Q

B Q = 27 cm

and

C Q = C R

.
Therefore,
Question Image

All the angles in quadrilateral DROS are right angles. Therefore, DROS is a rectangle.
We know that opposite sides of the rectangle are equal.
Therefore,

O S = R D

i.e.,

R D = 10 c m

.
Then, the value of CD is,
Question Image

Hence, the length of CD is

21 cm

.
Therefore, option 4 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th