幾何與角

In the figure, $ABCD$ is a square. If $CEF$ is an equilateral triangle, then $\angle CBF=$

In the figure, $x=$

In the figure, $OABC$ and $OFED$ are straight lines. If $AB:BC=2:3$ and $FA:DC=1:5$, then $OA:AB=$

In the figure, $ACE$ and $BDF$ are straight lines. If the areas of the quadrilaterals $ABDC$ and $CDFE$ are $16\text{ cm}^2$ and $5\text{ cm}^2$ respectively, then the length of $AB$ is

In the figure, $AB$ and $AC$ are tangents to the circle at $X$ and $Y$ respectively. $Z$ is a point lying on the circle. If $\angle BAC=100^\circ$, then $\angle XZY=$

In the figure, $O$ is the centre of the circle and $AOC$ is a straight line. If $AB$ and $BC$ are tangents to the circle such that $AB=3$ and $BC=4$, then the radius of the circle is

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, $ABCD$ is a parallelogram and $E$ is a point on $AD$ such that $AE:ED=1:3$. If the area of $\triangle ABE$ is $3\text{ cm}^2$, then the area of the shaded region is

In the figure, $AD$ and $BC$ meet at $E$. If $CE:EB=3:1$, then area of $\triangle ABD$ : area of $\triangle CDE=$