幾何與角

In the figure, $O$ is the centre of the circle $ABCD$. If $EAB$ and $EDOC$ are straight lines and $EA=AO$, find $\angle AEO$.

In the figure, $O$ is the centre of the circle $ABC$. Find $x$.

In the figure, $ABCD$ is a circle. $AC$ and $BD$ meet at $E$. If $AD=4$, $AE=2$, $EC=5$ and $BE=4$, then $BC=$

In the figure, $ABC$ is a circle. If $\angle ABC=30^\circ$ and $\widehat{AC}=4$, then the circumference of the circle is

In the figure, $ABC$ is a straight line. If $BD /\!/ CE$, then $\angle DCE=$

In the figure, $ABCD$ and $AGFE$ are straight lines. If $BC=2\text{ cm}$, $CD=3\text{ cm}$, $BG=6\text{ cm}$ and $CF=10\text{ cm}$, then $DE=$

In the figure, $ABCD$ is a circle. If $\widehat{CD}=2\widehat{DA}=2\widehat{AB}=2\widehat{BC}$, then $x=$

In the figure, $TS$, $SQ$ and $QP$ are tangents to the circle at $T$, $R$ and $P$ respectively. If $TS /\!/ PQ$, $TS=3$ and $QP=12$, then the radius of the circle is

In the figure, $ABDF$ and $ACEG$ are straight lines. If the area of $\triangle ABC$ is $16\text{ cm}^2$ and the area of quadrilateral $BDEC$ is $20\text{ cm}^2$, then the area of quadrilateral $DFGE$ is

In the figure, $AEDC$ is a parallelogram. If $AB:BC=1:2$ and $AF:FE=2:1$, then area of $\triangle ABF$ : area of $\triangle BCD=$