the following are the relationships between 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