幾何與角

In the figure, $O$ is the centre of the smaller circle. $OAB$ and $PQR$ are straight lines. Find $\theta$.

In the figure, $B$ is the mid-point of arc $AC$. $AC=AD$. If $\angle ADC=56^\circ$, then $\angle BCD=$

In the figure, $ABCD$ is a parallelogram. $E$ and $F$ are the mid-points of $AB$ and $DC$ respectively. $BF$ and $ED$ cut $AC$ at $P$ and $Q$ respectively. If the area of $ABCD$ is 48, find the area of the shaded part.

In the figure, $AC$ cuts $BD$ at $O$. The areas of $\triangle AOB$, $\triangle AOD$ and $\triangle BOC$ are $7\text{ cm}^2$, $12\text{ cm}^2$ and $10.5\text{ cm}^2$ respectively. Find the area of $\triangle OCD$.

$ABCD$ is a cyclic quadrilateral with $AB=AD$ and $CB=CD$. Find $\angle ABC$.

In the figure, $O_1$ and $O_2$ are the centres of the two circles, each of radius $r$ and $AB=\sqrt{12}$. Find $r$.

In the figure, $ABCD$ is a parallelogram. $AB\perp BD$, $AB=3$ and $BC=5$. $AC=$

In the figure, chords $AC$ and $BD$ meet at $E$ and $AB\parallel DC$. If $\angle CED=104^\circ$, find $\angle ABD$.

In the figure, $AB$, $BC$ and $CD$ are three equal chords of a circle. If $\angle BAC=a$, then $\angle AED=$

In the figure, $ABCD$ and $ABEF$ are parallelograms. $\dfrac{\text{Area of }ABCD}{\text{Area of }ABEF}=$