In the given figure, a circle is inscribed in a ΔABC, 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.

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Solution

Given that,
AB = 12 cm
BC = 8 cm
CA = 10 cm

Now, lets divide tangents into parts for and get equations using the provided informations.
i.e.
Now,
AB = y + z = 12 cm ----- ( i )
BC = z + x = 8 cm -------- ( ii )
CA = x + y = 10 cm -------- ( iii )

On solving (i), (ii) and (iii)
we get,
x = 3 cm = CF
y = 7 cm = AD
z = 5 cm = BE

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