10th Class
Mathematics
Circles
Question Bank
Circles
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) \[x+(1+w)=4\] \[\Rightarrow \] \[x+w=3\] \[\Rightarrow \] \[AD=3\,cm\]