question_answer

In Fig. 2, a circle is inscribed in a \[\Delta \,ABC\], such that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.

Answer:

Given, \[AB=12\text{ }cm;\text{ }BC=8\text{ }cm\] and \[CA=10\text{ }cm\]

Let                    \[AD=AF=x\]

\[\therefore DB=BE=12-x\]

and,                  \[CF=CE=10-x\]

Now,                 \[BC=BE+EC\]

\[\Rightarrow 8=12-x+10-x\]

\[\Rightarrow 8=22-2x\]

\[\Rightarrow 2x=14\]

\[\Rightarrow x=7\text{ }cm\]

\[\therefore \,\,~AD=7\text{ }cm,\text{ }BE=5\text{ }cm\] and \[CE=3\text{ }cm\]