已知: 如图, $\angle A=\angle D=90^{\circ}, A C=B D$. 求证: $O B=O C$.

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证明: $\because \angle A=\angle D=90^{\circ}$,

$\therefore$ 在 Rt $\triangle A B C$ 和 Rt $\triangle D C B$ 中,

$\left\{\begin{array}{l}B C=C B \\ A C=B D\end{array}\right.$

$\therefore$ Rt $\triangle A B C \cong$ Rt $\triangle D C B(\mathrm{HL})$,

$\therefore \angle A C B=\angle D B C$.

$\therefore O B=O C$.