1988 年

$ABCD$ is a square of side $2\text{ cm}$. $O$ is the mid-point of $AD$. A sector with centre $O$ is inscribed in the square as shown in the figure. What is the area of the sector?

In the figure, $ABCD$ is a G-shaped curve, where $ABC$ is an arc of a circle and $DC$ is a radius. If the length of the curve $ABCD$ is the same as that of the complete circle, find, in radians, the angle subtended by the arc $ABC$ at the centre.

$ABCD$ is a cyclic quadrilateral with $AB=AD$ and $CB=CD$. Find $\angle ABC$.

In the figure, $O_1$ and $O_2$ are the centres of the two circles, each of radius $r$ and $AB=\sqrt{12}$. Find $r$.

In the figure, $ABCD$ is a parallelogram. $AB\perp BD$, $AB=3$ and $BC=5$. $AC=$