Q20 of 52 Page 10

In Fig. 2, 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. (CBSE 2016)

The figure can be redrawn as follows:


It is given in the question that,


AB = 12 cm


BC = 8 cm


AC = 10 cm


As we know that, tangents drawn from an external point in a triangle are equal


∴ AF = AD, CF = CE, BD = BE


Let us assume AD = AF = x cm


∴DB = AB – AD


= (12 – x) cm


Also, BE = (12 – x) cm


Similarly,


CF = CE = AC – AF


= (10 – x) cm


As, BC = 8 cm


∴ BE + CE = 8


12 – x + 10 – x = 8


22 – 8 = 2x


2x = 14


x = 7 cm


Hence, AD = x = 7 cm


BE = 12 – x


= 12 – 7


= 5 cm


And, CF = 10 – x


= 10 – 7


= 3 cm

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