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               \[2(x+y+z)=50\] \[\Rightarrow \] \[x+y+z=25\]