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Question

# 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

A

5cm, 9cm and 4cm

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B

3cm, 7cm and 5cm

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C

4cm, 6cm and 8 cm

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D

2cm, 6cm and 7cm

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Solution

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