A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be

5cm, 9cm and 4cm

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3cm, 7cm and 5cm

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4cm, 6cm and 8 cm

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2cm, 6cm and 7cm

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Solution

The correct option is B
3cm, 7cm and 5cm

We know that the tangents from an external point are equal.
Let AD = AF = x cm, BD = BE = y cm and CE = CF = z cm
x + y = AB = 10 cm (1)
y + z = BC = 12 cm (2)
z + x = CA = 8 cm (3)
Adding the above equations,
2(x + y + z) = 30 or x + y + z = 15 (4)
From (1) and (4): z = 5

From (2) and (4): x = 3

From (3) and (4): y = 7
Hence, AD = 3 cm, BE = 7 cm and CF = 5 cm

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