1989 年

In the figure, $C$ is the centre of the circle $x^2+y^2-6x-8y+21=0$. $OA$ and $OB$ are tangents. If $\angle AOB=2\theta$, find $\sin\theta$.

In the figure, $ABCD$ and $WXYZ$ are sectors of equal radii. If arc $BCD$ : arc $XYZ=s:t$, then which of the following is/are true?

In the figure, $O$ is the centre of two concentric circles. $AB$ is tangent to the smaller circle. If $AB=2$, find the area of the shaded part.

If 10 arithmetic means are inserted between $a$ and $b$, then the last one is

Given that $y\propto\dfrac{1}{x}$, if $x$ increased by $25\%$, find the percentage change in $y$.

The costs of two kinds of coffee $A$ and $B$ are $\$12$/kg and $\$20$/kg respectively. In what ratio by weight should $A$ and $B$ be mixed so that the mixture will cost $\$15$/kg?

In the figure, $D$ and $E$ are points on $AB$ and $AC$ respectively such that $\angle ABC=\angle AED$, $AD=8$, $AE=5$ and $EC=15$. If the area of $\triangle ADE$ is 16, then the area of the quadrilateral $BCED$ is

In the figure, $O$ is the centre of the circle of radius 6 cm. The area of the shaded part is

If the sum to infinity of the G.P. $1,-t,t^2,-t^3,\dots$ is $\dfrac{2}{3}$, find the fourth term.

If $\dfrac{x+3y}{2x+y}=2$, find $\dfrac{3x+y}{x+2y}$.