2005 年

In the figure, $ABCD$ is a circle. If $\widehat{AB}:\widehat{BC}:\widehat{CD}:\widehat{DA}=1:2:3:3$ and $E$ is a point lying on $BD$, then $\angle CAE=$

In the figure, $ABCD$ is a parallelogram. $E$, $F$ and $G$ are points lying on $BC$, $CD$ and $DA$ respectively. $AE$ and $AF$ divide $\angle BAD$ into three equal parts and $BG$ bisects $\angle ABC$. If $AE$ and $AF$ intersect $BG$ at $H$ and $I$ respectively, then $\angle GIF+\angle GHE=$

In the figure, $O$ is the origin. If the equation of the circle passing through $O$, $A$, $B$ and $C$ is $(x+3)^2+(y-4)^2=25$, then the area of the rectangle $OABC$ is

In the figure, the circle passing through $A(0,8)$ and $B(0,2)$ touches the positive $x$-axis. The equation of the circle is