Question

In Fig. 10.54, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.

Answer 1

Answer:

here

AP=AS(tangents drawn from an external points are equal)

let , AP =AS=x

similarly,BP=BQ

CQ=CR

RD=DS

since,AP=x

BP=AB-AP=6-x

now,BP=BQ=6-x

CQ=BC-BQ-7-(6-x)

=7-6+x

=1+x

now,

CQ=CR=1+x

RD=CD-CR=4-(1+x)

=4-1-x=3-x

now,RD=DS=3-x

AD=AS+SD

=x+3-x=3

AD=3.

hope this helps you!!