A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the point P, Q, R and S, respectively and ∠B = 90°. If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 18π.
Given: ∠B = 90°, AD = 24 cm, AB = 27 cm and DR = 6 cm.
In the figure:
DS = DR = 6 cm [Length of tangents to a circle from a same point are equal]
So,
AS = AD - DS = 24 - 6 = 18 cm
So, AP = AS = 18 cm
Now,
PB = AB - AP = 27 - 18 = 9 cm
Since, ∠B = 90° and ∠OPB = 90°
Radius of the circle = 9 cm
Hence,
Circumference of the circle = 2πr = 2π(9) = 18π