幾何與角

In the figure, $ABCD$, $AFE$, $CGE$ and $FGD$ are straight lines. If $AB=BC=2CD$, then $CG:GE=$

In the figure, find $x$.

In the figure, $ABCDE$ is a regular pentagon and $ABF$ is an equilateral triangle. Find $\theta$.

In the figure, $EC$ is the tangent to the circle at $C$. Find $\angle CBD$.

In the figure, $AC$ is the angle bisector of $\angle BAD$. Which of the following statements must be true? I. $\triangle BCE\sim\triangle ADE$ II. $\triangle ABC\sim\triangle AED$ III. $\triangle ABC\sim\triangle BDA$

In the figure, $\overset{\frown}{AB}=2$, $\overset{\frown}{BC}=3$, $\overset{\frown}{CD}=4$ and $\overset{\frown}{DA}=6$. Find $\angle BCD$.

In the figure, $ABCD$ is a parallelogram. $PDC$, $PQRS$ and $ABS$ are straight lines. If $AQ=4$, $QD=2$ and $BR=RC=3$, then $PQ:QR:RS=$

In the figure, $ABCD$ is a rectangle. $CDE$ is a straight line and $AE\parallel BD$. If the area of $ABCD$ is $24$ and $F$ is a point on $BC$ such that $BF:FC=3:1$, find the area of $\triangle DEF$.

In the figure, $AB\parallel DC$. If the areas of $\triangle ABE$ and $\triangle CDE$ are $4$ and $9$ respectively, find the area of $\triangle BCE$.

In the figure, area of $\triangle ACD$ : area of $\triangle BCD=$