幾何與角

According to the figure, which of the following must be true?

In the figure, $O$ is the centre of the circle $ABCD$. If $\angle ADC=84^\circ$ and $\angle CBO=38^\circ$, then $\angle AOB=$

In the figure, $AB$ is the tangent to the circle at $B$ and $ADC$ is a straight line. If $AB:AD=2:1$, then the area of $\triangle ABD$ : the area of $\triangle BCD=$

In the figure, $ABCD$ is a parallelogram. $E$ is a point lying on $AB$. If $EC$ and $BD$ intersect at $F$, then the ratio of the area of $\triangle DEF$ to the area of $\triangle CBF$ is

Which of the following plane figures have rotational symmetry?

In the figure, the square $ABCD$ is divided into nine identical squares and four of them are shaded. The number of axes of reflectional symmetry of the square $ABCD$ is

If the sum of the interior angles of a convex $n$-sided polygon is $4$ times the sum of the exterior angles of the polygon, then $n=$

In the figure, $AY$ and $CY$ are the angle bisectors of $\angle BAX$ and $\angle DCX$ respectively. If $\angle AXC=100^\circ$, then $\angle AYC=$

If the point $(3,-2)$ is rotated clockwise about the origin through $90^\circ$, then the coordinates of its image are

In the figure, $A$, $B$, $C$ and $D$ are points lying on the circle. If $AB=5$, $AD=3$ and $BD=7$, then $\angle BCD=$