證明：?$(1)$?∵?$AB=CD$?
∴?$\widehat {AB}=\widehat {CD}$?
∴?$\widehat {AC}+\widehat {CB}= \widehat {CB}+\widehat {DB}$?
∴?$\widehat {AC}=\widehat {BD}$?
解：?$(2)$?∵?$\widehat {AC}=\widehat {BD}$?
∴?$∠ADC=∠BAD$?
∴?$∠AMC=∠MAD+∠MDA=2∠BAD$?
∵?$AD$?是?$⊙O$?的直徑
∴?$∠ACD=90°$?
∴?$∠CAB+ ∠AMC=90°$?
∴?$∠AMC=90°- ∠BAC=54°$?
∴?$∠BAD=\frac {1}{2}∠AMC=27°$?
