Question

The area of the triangle inscribed in a circle of radius of 4 and the measures of whose angles are in the ratio 5:4:3 is

(A)  4(3 + √3)

(B)  4(√3 + √2)

(C)  4(3 - √3)

(D)  4(√3 - √2)

Answer 1

Correct option  (A)  4(3 + √3)

See Fig

 Angle at circumference = Half of centre

Δ = 1/2 x (2√3 + 6) x 4 = 4(√3 + 3)

Angles of ∆: 75, 60, 45. Now,

Area = 1/2 absinC = 1/2.2R.2R.sinA.sinB.sinC