幾何與角

In the figure, the three sides of $\triangle ABC$ touch the circle at the points $P$, $Q$ and $R$. $\angle PQR=$

In the figure, $ABCD$ is a quadrilateral with $AB=BC$ and $AD=DC$. Which of the following is/are true? I. $\angle BAD=\angle BCD$ II. $AC\perp BD$ III. $BD$ bisects $AC$

In the figure, $X$ and $Y$ are points on $AB$ and $BC$ respectively such that $AX:XB=3:2$ and $BY:YC=4:3$. If the area of $\triangle ABC=70$, then the area of $\triangle AXY=$

In the figure, chords $AB$ and $CD$ intersect at $E$. The length of the minor arc $BD$ is three times the length of the minor arc $AC$. $\angle BAD=$

In the figure, $PQ$ and $XY$ touch the circle at $A$ and $B$ respectively. $PQ\parallel XY$ and $\angle QAC=60^\circ$. $\angle CBX=$

In the figure, $x=$

In the figure, $ABCD$ is a square and $PAB$ is an equilateral triangle. $\angle CPD=$

In the figure, $AEC$ and $BED$ are two chords of the circle. $\angle CBD=$

In the figure, $PQ$ and $RS$ touch the circle at $A$ and $C$ respectively. $\angle ABC=$

In the figure, the rectangles are similar. $PQ=a$, $QR=b$. If $AC=2PR$, what is the area of $ABCD$?