A circle inscribed in a triangle ABC having sides BC=8 cm, AC= 10 cm and AB=12cm. Find AD,BE & CF

A circle inscribed in a triangle ABC having sides BC=8 cm, AC= 10 cm a

1.	A circle inscribed in a triangle ABC having sides BC=8 cm, AC= 10 cm and AB=12cm. Find AD,BE & CF
Answer» Tangents drawn from an external point to a circle are equal.{tex}\\Rightarrow{/tex}\xa0AD = AF, BD = BE, CE = CF.\xa0Let AD = AF =\xa0aBD = BE =\xa0b\xa0CE = CF =\xa0c AB = AD + DB =\xa0a\xa0+\xa0b\xa0= 8 ........ (1)BC = BE + EC =\xa0b\xa0+\xa0c\xa0= 10 ........ (2)AC = AF + FC =\xa0a\xa0+\xa0b\xa0= 12 ........ (3)\xa0Adding (1), (2) and (3), we get2 (a\xa0+\xa0b\xa0+\xa0c) = 30{tex}\\Rightarrow{/tex}\xa0(a\xa0+\xa0b\xa0+\xa0c) = 15 ........ (4)Subtracting (1) from (4), we get\xa0c\xa0= 7Subtracting (2) from (4), we get\xa0a\xa0= 5Subtracting (3) from (4), we get\xa0b\xa0= 3Therefore, AD =\xa0a\xa0= 5 cm, BE =\xa0b\xa0= 3 cm, CF =\xa0c\xa0= 7 cm