1983 年

In the figure, $BC=a$. $AB=$

In the figure, $ABCD$ is a rectangle. $AB=p$ and $BC=q$. If $\angle BAY=\theta$, the distance of $C$ from the line $XAY$ is

If $0^\circ\le\theta<360^\circ$, the number of roots of the equation $4\sin^2\theta\cos\theta=\cos\theta$ is

The maximum value of $\cos^2 3x$ is

The figure above shows the graph of a tangent function from $0^\circ$ to $360^\circ$. The function is

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 $\angle QAC=60^\circ$. $\angle CBX=$