# A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and

| A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S respectively, and ∠B = 90

^{o}. If AD = 24 cm, AB = 27 cm and DR = 6cm, then what is the circumference of the circle?A. 15 π

B. 20 π

C. 12 π

D. 18 π

### Right Answer is: D

#### SOLUTION

AD = 24cm, AB = 27cm, DR = 6cm.

SD = DR = 6cm (∵ SD and DR are tangents)

AS = 24 – 6 = 18cm

AP = AS = 18cm (∵ AP and AS are tangents)

PB = 27 – 18 = 9cm

∠P = ∠Q = 90^{o}

PB = PQ = *r* = 9cm

Circumference of the circle = 2π*r*

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A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and