Mathematics - Properties of Triangle Question with Solution | TestHub

A tangent segment from a vertex of angle X to its contact has length cot(X/2) for radius 1. Therefore AB=cot(A/2)+cot(B/2)=sin[(A+B)/2]/[sin(A/2)sin(B/2)]. Likewise CD=sin[(C+D)/2]/[sin(C/2)sin(D/2)]. Since A+B+C+D=2$\pi$, the two numerator sines coincide, proving B.