Find Circle between 2 Circle and Line(Heron's formula)

Area of Pink
( GB * EN ) / 2 = ( H * GQ ) / 2[br][br]海龍公式[br]s = [ ( R + r ) + ( R + x ) + ( r + x ) ] / 2[br]= R + r + x[br][br]N = (Qx,Qy)+r(cosθ,sinθ)[br]E = (Ax,Ay)+R(cosθ,sinθ)[br]線段NE的平方 = (R+r)(R+r) - (R-r)(R-r)[br]化簡後可得 0 = (r-R)+(Qx-Ax)cosθ+(Qy-Ay)sinθ[br]移項後有 (R-r)-(Qy-Ay)sinθ = (Qx-Ax)cosθ[br]即 g(θ) = f(θ)
– WC

Information: Find Circle between 2 Circle and Line(Heron's formula)