10th Class
Mathematics
Circles
Question Bank
Circles
question_answer
A circle inscribed in \[\Delta \,ABC\] having \[AB=10\text{ }cm,\]\[BC=12\text{ }cm,\text{ }CA=28\text{ }cm\]touching sides at D, E, F (respectively). Then \[AD+BE+CF\]is _____.
A)25 cm
B) 20 cm
C) 22 cm
D) 18 cm
Correct Answer:
A
Solution :
\[x+y=10\text{ }cm\] ?...(i) \[y+z=12cm\] ?..(ii) \[x+z=28cm\] .....(iii) Adding (i), (ii) and (iii), we get \[2(x+y+z)=50\] \[\Rightarrow \] \[x+y+z=25\]