幾何與角

In the figure, the regular hexagon is divided into six equilateral triangles and two of them are shaded. The number of folds of rotational symmetry of the hexagon is

The coordinates of the point $A$ are $(-3,3)$. If $A$ is reflected with respect to the straight line $x=1$ to the point $B$, then the distance between $A$ and $B$ is

In the figure, $AB$ is a diameter of the circle $ABCD$. It is given that $AC$ and $BD$ intersect at $E$. If $\angle AED=\theta$, then $\dfrac{CD}{AB}=$

In the figure, $ABCD$ is a circle. If $AB=AC$, $AB\parallel DC$ and $\angle ABD=40^\circ$, then $\angle CBD=$

In the figure, $AB$ is the tangent to the circle at $A$. If $AB=20$ and $BC=50$, find the radius of the circle.

In the figure, $G$ is the centroid of $\triangle ABC$. $AG$, $BG$ and $CG$ are produced to meet $BC$, $AC$ and $AB$ at $L$, $M$ and $N$ respectively. If $BL=13\text{ cm}$, $BN=5\text{ cm}$ and $CM=12\text{ cm}$, find the area of $\triangle ABC$.

In the figure, $ABCD$ is a parallelogram. $M$ is a point lying on $BC$ such that $BM:MC=1:2$. If $BD$ and $AM$ intersect at $G$ and the area of $\triangle BGM$ is $1\text{ cm}^2$, then the area of the parallelogram $ABCD$ is

If the plane figure above is rotated anticlockwise about the point $O$ through $135^\circ$, which of the following is its image?

Which of following triangles have reflectional symmetry but do not have rotational symmetry?

In the figure, $AB\parallel CD$ and $AC=BD$. If $\angle CAD=20^\circ$ and $\angle ADB=80^\circ$, then $\angle ADC=$