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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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