The following are the relationships between the relevant angles and sides:

• Angle ACE = Angle ECD = ½ Angle ACD

• Angle ACO = 90º - ½ Angle BAC

• Angle OCE = Angle ACE - ACO

• OE = ½ line BC x tan (OCE)

• AE = OA + OE

• ED = AD -AE

• Line EDF = ½ Line BDC

• EF = sin (EDF) x ED