?$證明：(1)∵AE⊥AC，BD垂直平分AC$?
$∴AE//BD$?
?$∵∠ADE=∠BAD$?
$∴DE//AB$?
?$∴四邊形ABDE是平行四邊形$?
?$(2)∵DA平分∠BDE$?
?$∴∠ADE=∠BDA$?
?$∵∠ADE=∠BAD$?
?$∴∠BAD=∠BDA$?
?$∴AB=BD=5$?
?$設(shè)BF=x，DF=5-x$?
?$在Rt△ABF 中，5^2-x^2=AF^2$?
?$在Rt△ADF 中，6^2-(5-x)^2=AF^2$?
?$∴5^2-x^2=6^2-(5-x)^2$? ?$解得x=\frac 75$?
?$∴AF=\sqrt{AB^2-BF^2}=\sqrt{5^2-(\frac 75)^2}=\frac {24}5$?
