Problem 463: Three Concentric Circles, Secant, Tangent, Triangle, Area

Problem 463. The figure shows three concentric circles C₁, C₂, and C₃, with center O. Line ABC is a secant to circles, OD is perpendicular to line ABC extended, line AEF is tangent to circle C₁ at A, line BGF is tangent to circle C₂ at B, and line CGE is tangent to circle C₃ at C. If AB = a, BC = b, and OD = c, prove that the area of triangle EFG is .