1994 年

In the figure, $O$ is the centre of the circle. If $AC=3$ and $\angle BAC=\dfrac{\pi}{6}$, find the diameter $AB$.

In the figure, $PA$ is tangent to the circle at $A$, $\angle CAP=28^\circ$ and $BA=BC$. Find $x$.

In the figure, $O$ is the centre of the inscribed circle of $\triangle ABC$. If $\angle OAC=30^\circ$ and $\angle OCA=25^\circ$, find $\angle ABC$.

In the figure, $AB=AD$ and $BC=CD$. If $\angle BAD=80^\circ$ and $\angle ADC=65^\circ$, then $\angle BCD=$

In the figure, $x$, $y$ and $z$ are the exterior angles of $\triangle ABC$. If $x:y:z=4:5:6$, then $\angle BAC=$

The points $A(4,-1)$, $B(-2,3)$ and $C(x,5)$ lie on a straight line. Find $x$.

In the figure, the shaded part is bounded by the axes, the lines $x=3$ and $x+y=5$. Find its area.

$AB$ is a diameter of the circle $x^2+y^2-2x-2y-18=0$. If $A$ is $(3,5)$, then $B$ is

The equations of two circles are $\begin{cases} x^2+y^2-4x-6y=0 \\ x^2+y^2+4x+6y=0 \end{cases}$. Which of the following is/are true?

I. The two circles have the same centre. II. The two circles have equal radii. III. The two circles pass through the origin.

In the figure, the pie chart shows the monthly expenditure of a family. If the family spends $\$4\,800$ monthly on rent, what is the monthly expenditure on entertainment?