幾何與角

In the figure the circle touches the sides of $\triangle ABC$ at $X$, $Y$ and $Z$. $O$ is the centre of the circle. Which of the following must be true?

I. $OA$ bisects $\angle BAC$ II. $A$, $X$, $O$ and $Z$ are concyclic III. $AX=AZ$

The sum of the interior angles of a convex polygon is greater than the sum of the exterior angles by $360^\circ$. How many sides has the polygon?

In the figure, $x=$ ?

In the figure, $O$ is the centre of the circle. $TA$ and $TB$ touch the circle at $A$ and $B$ respectively. $OA=2$. The length of the arc $APB$ is

In the figure, $XY\parallel BC$. $AX:XB=2:1$. If the area of the trapezium $BCYX=20$, then the area of $\triangle ABC=$

In the figure, $AB$ is a diameter of the circle. $AP=AQ$. $AB=10$ and $BP=8$. $PQ=$

In the figure, the chords $BA$ and $CD$, when produced, meet at $P$. The chords $AD$ and $BC$, when produced, meet at $Q$. $\angle B=$

In the figure, $D$ is a point on $BC$ and $AC=AD=BD$. $\angle CAD=$

The sum of the six marked angles in the figure is

In the figure, chords $AB$ and $CD$ intersect at $P$. $BP=DP$. $\angle CAD=$