The attached figure was constructed as follows:

Given TriangleABCextendACtoEsuch thatAE=AE1.AD1 is the angle bisector of AngleBAEandADis the angle bisector of AngleBAC.Ois the midpoint ofDD1.AD//EBandE1B//AD1. ArcDAD1 is drawn.

I know that the following ratios exist:

AC/AE=DC/DB

AC/AE1 =D1C/D1B

DC/DB=D1C/D1B

LetCO=u,BO=v, and (1/2)DD1 =R. Prove thatu*v=R^2