幾何與角

In the figure, $BP$ is a diameter of the circle. The minor arc $AB$ and the radius are of equal length. $\angle APB=$

In the figure, $O$ is the centre of the circle. $PQ$ is a diameter. Which of the following is/are true? I. $a=b$ II. $c=2a$ III. $c+d=180^\circ$

In the figure, the length of the minor arc $CD$ is half the length of the minor arc $BC$. $\angle ACD=$

In the figure, $TP$ and $TQ$ touch the circle at $P$ and $Q$ respectively. $R$ is the point on $TQ$ produced such that $PR$ passes through the centre $O$ of the circle. $\angle QPR=$

In the figure, $AT$ touches the circle at $A$. In $\triangle ABC$, $\angle A:\angle B:\angle C=2:3:4$. $\theta=$

In the figure, $AB$ is a diameter of the circle with centre at $O$. The length of the minor arc $AC$ is twice the length of the minor arc $CD$. $\angle BOD=$

In the figure, two circles both with radius $2\text{ cm}$ touch each other externally. $AP$ and $AQ$ are equal tangents to the two circles. $AP=$ ?

In the figure, $ABC$ is an equilateral triangle of side $2a$. $P$ and $Q$ are the mid-points of $AB$ and $AC$ respectively. $PQRS$ is a rectangle. What is the area of $PQRS$?

In the figure, $AB$ and $AC$ touch the circle at $B$ and $C$. If $P$ is any point on the minor arc $BC$, what is $\theta$?

In the figure, $AB\parallel CD\parallel EF$. $ACF$, $BCE$ and $BDF$ are straight lines. $AB=12$, $EF=6$. $CD=$ ?