SemicirclesC1,C2,C3 are described externally on the sides BC, CA and AB of triangle ABC(with usual notations) as diameter respectively. If l1,l2,l3be the length of common tangents to C2,C3,C3,C1,andC1,C2respectively, then l1l2l3 is

l1=a22−b−c22   since length of the direct common tangent of two circles having radius r1,r2 is d2-r1-r22where d= distance between centres l 12=a+b−c2a−b+c2l 12=s−cs−b,l 22=s−as−c,l 32=s−as−bl1l2l32=s−a2s−b2s−c2l1l2l3=s−as−bs−cl1l2l3=Δ2s