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 \[CE=3\text{ }cm\]
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