证明：连接$OE，$设$∠ D=x。$
$\because OB=OE，$
$\therefore ∠ B=∠ OEB。$
$\because ∠ OEB$是$△ DEO$的外角，
$\therefore ∠ OEB=∠ D+∠ DOE=x+∠ DOE。$
$\because ∠ AOB$是$△ BOD$的外角，
$\therefore ∠ AOB=∠ B+∠ D=∠ OEB+∠ D=x+∠ DOE +x=∠ DOE +2x。$
$\because ∠ AOB=3∠ D=3x，$
$\therefore ∠ DOE+2x=3x，$即$∠ DOE=x=∠ D，$
$\therefore DE=OE，$
$\therefore DE=OB$
