Question

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm, CD = 4 cm. Find the length of AD.

• A. $10cm$
• B. $11cm$
• C. $13cm$
• D. $3cm$

Answer 1

Answer: (D)

$AS$ and $AP$ are tangents drawn from $A$ to the circle

$⟹AS=AP$

Similarly

$DS=DR,RC=CQ,QB=BP$

$AB=AP+PB=6$

$AP=6-PB$

$BC=BQ+QC=7cm$

$CD=CR+DR=4cm$

$AD=AS+SD=AP+RD$

$=(6-PB)+(4-CR)$

$=10–(PB+CR)$

$=10–(BQ+CQ)=10-BC$

$=10–7=3cm$