如图四边形ABCD中,角BAD=角BCD=90度,AB=AD。(1)求证:AC平分角BCD (2...答:∵∠BAD=90度,且AB=AD,∴∠DBA=45度,OA=OB,∴∠DAB=∠DBA=45度,△ABC中,∠ABC+∠BCA+∠CAB=∠OBA+∠OBC+∠BCA+∠CAO+∠OAB=2∠BCA+90度=180度 ,∴∠BCA=45度,∵∠BCD=90度,∴AC平分∠BCD 2)∵∠BAD=∠BCD=90度,∴AB^2+AD^2=2AB^2=BC^2+CD^2=116,∴AB=√58 ...