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