$證明：(1)∵AE⊥AC，BD垂直平分AC?$
$∴AE//BD?$
$?∵∠ADE=∠BAD?$
$∴DE//AB?$
$?∴四邊形ABDE是平行四邊形?$
$?(2)∵DA平分∠BDE?$
$?∴∠ADE=∠BDA?$
$?∵∠ADE=∠BAD?$
$?∴∠BAD=∠BDA?$
$?∴AB=BD=5?$
$?設BF=x，DF=5-x?$
$?在Rt△ABF 中，5^2-x^2=AF^2?$
$?在Rt△ADF 中，6^2-(5-x)^2=AF^2?$
$?∴5^2-x^2=6^2-(5-x)^2? ?解得x=\frac 75?$
$?∴AF=\sqrt{AB^2-BF^2}=\sqrt{5^2-(\frac 75)^2}=\frac {24}5?$
$?∴AC=2AF=\frac{48}{5}$
