A circle is inscribed in triangle ABC and touches the sides BC, CA and AB at D, E and F respectively. If AB = 12 cm, BC = 14 cm and CA = 16 cm, what is the length of BD?

Question

Accepted Answer

5 cm. Tangents from a point are equal, so let AE = AF = x, BF = BD = y and CD = CE = z. Then x + y = 12, y + z = 14 and z + x = 16. Adding gives 2(x + y + z) = 42, so x + y + z = 21. Therefore z = 21 − 12 = 9, x = 21 − 14 = 7 and y = 21 − 16 = 5. So BD = 5 cm (while DC = 9 cm).

A circle is inscribed in triangle ABC and touches the sides BC, CA and AB at D, E and F respectively. If AB = 12 cm, BC = 14 cm and CA = 16 cm, what is the length of BD?

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