证明：延长$AD$交$\odot O$于点$E。$
因为$AD\perp OC，$根据垂径定理，可得$\overset{\frown}{EC}=\overset{\frown}{AC}，$$AD = DE，$所以$\overset{\frown}{AE}=2\overset{\frown}{AC}，$$AE = 2AD。$
又因为$\overset{\frown}{AB}=2\overset{\frown}{AC}，$所以$\overset{\frown}{AB}=\overset{\frown}{AE}，$所以$AB = AE，$所以$AB = 2AD。$
