63. Two circles touch each other internally at point $A$. From the center of the larger circle, a radius $O B$ is drawn, touching the smaller circle at point $C$. Find $\widehat{B A C}$.
63. If $O_{1}$ is the center of the smaller circle, and $\widehat{B O A}=\varphi$, then $\widehat{B A O}=90^{\circ}-\frac{\varphi}{2}$, $\widehat{C O_{1} A}=90^{\circ}+\varphi$, $\widehat{C A O_{1}}=45^{\circ}-\frac{\varphi}{2}$. Therefore,

$$
\begin{gathered}
\widehat{B A C}=\widehat{B A O}-\widehat{C A O_{1}}=45^{\circ} . \\
\text { Answer: } 45^{\circ} .
\end{gathered}
$$