Question

If the lengths of arcs AB, BC and CA of a circle are 3, 4 and 5, respectively, then the area of triangle ABC is

(A)  9√3(√3 + 1)/π²

(B)  9√3(√3 - 1)/π²

(C)  9√3(√3 - 1)/π

(D)  None of these

Answer 1

Correct option (A)  9√3(√3 + 1)/π²

See Fig. Angle subtended by the chord AB, BC and CA at centre of circle is in ratio 3:4:5, that is, 90°, 120°, 150°. So,

∠B = 75°, ∠C = 45°, ∠A = 60°. 

Perimeter of circle, 2π r = 12

r = 12/2π = 6/π

Area of triangle = 2r² sin A sinB sinC