Question

Consider a ∆ABC and let a, b and c denote the lengths of the sides opposite to vertices A,B,C respectively. Suppose a = 6, b = 10 and the area of the triangles is 15√3 . If ∠ACB is obtuse and if r denotes the radius of the in circle of the triangle, then r² is equal to………

Answer 1

∆ = 1/2absinCsinC = 2∆/ab = (2 x 15√3/(6 x 10) = √3/2C = 120°

⇒ c = √(a² + b² - 2abcosC)

= √(6² + 10² - 2 x 6 x 10 x cos120°) = 14

r = ∆/s ⇒ r² = (225 x 3)/((6 + 10 + 14)/2) = 3