Correct option (C) 4∆/R2
Explanation:
∠AOB = 2∠C = 2C
OA = OB = R
AB/sin∠ AOB = 2R1
R1 = c/2sin2c
L.H.S. = 2[sin2A + sin2B + sin2C]
= 2[2 sin(A + B) cos(A – B) + 2 sin C cos C]
= 4 sin C[cos(A – B) ± cos(A + B)] = 8 sinA sinB sinC
= 8(1/2absinC)(1/2bcsinA)(1/2casinB)
= 8a/a2b2c2 = 64∆3/a2b2c2 = 4∆/R2