A circle inscribed in a triangle has radius 4. Circle touches BC at D $ BD is 6 $ DC is 8 . Find the area of triangle

Dear Mayank

tanB/2 = 2/3

so sinB = 2tanB/2  / (1+ tan²B/2)  = 12/13

   cosB  = (1-tan²B/2)/(1+ tan²B/2) =5/13

tanC/2 = 1/2

so sinC = 2tanC/2  / (1+ tan²C/2)  = 4/5

   cosC  = (1-tan²C/2)/(1+ tan²C/2) =3/5

so sinA =sin(180- B-C) =sin(B+C) = sinBcosC +cosBsinC

                                                =56/65

so area of triangle = a² sinB sinC /2sinA       where a = 8+6 =14

                           =84

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