question_answer

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are \[AB=6\text{ }cm,\text{ }BC=7\text{ }cm,\]\[CD=4\text{ }cm,\]then AD equals _____.  

A) 10 cm             

B)        13 cm             

C)        11 cm             

D)        3 cm                                       

Correct Answer: D

Solution :

\[x+y=4cm\]              ?..(i) \[y+z=7\,cm\]                         ?...(ii)   \[z+w=6\,cm\]                        .....(iii)                Using (ii) and (iii),       \[y-w=1\]                Now using (i)          \[x+(1+w)=4\] \[\Rightarrow \]  \[x+w=3\]     \[\Rightarrow \] \[AD=3\,cm\]