Question

A circle touches all the four sides of a quadrilateral ABCD whose sides are $AB=6cm,BC=7cm$, and $CD=4cm$. What is the measure of AD?

• A. $14cm$
• B. $3cm$
• C. $7cm$
• D. $12cm$

Answer 1

The correct option is A $14cm$

Let $AP=x=AQ$

$\Rightarrow BP=6-x=BS$ $(asAB=6cm)$

$\Rightarrow CS=7-(6-x)=x+1=RC$ $(asBC=7cm)$

$\Rightarrow DR=4-(x+1)=3-x=QD$ $(asCD=4cm)$

And $QD+AQ=AD=3-x+x=3cm$