Question

A circle is inscribed in a abc with sides ac ab and bc as 8c 10cm and 12cm respect find the length ad be and ce

Answer 1

Sol: Tangents drawn from an external point to a circle are equal. ⇒ AD = AF, BD = BE, CE = CF. Let AD = AF = a BD = BE = b CE = CF = c AB = AD + DB = a + b = 8 -------- (1) BC = BE + EC = b + c = 10 -------- (2) AC = AF + FC = a + b = 12 -------- (3) Adding (1), (2) and (3), we get 2 (a + b + c) = 30 ⇒ (a + b + c) = 15 -------- (4) Subtracting (1) from (4), we get c = 7 Subtracting (2) from (4), we get a = 5 Subtracting (3) from (4), we get b = 3 Therefore, AD = a = 5 cm, BE = b = 3 cm, CF = c = 7 cm