1992 年

In the figure, $EB$ and $EC$ are the angle bisectors of $\angle ABC$ and $\angle ACD$ respectively. If $\angle A=40^\circ$, find $\angle E$.

In the figure, $O$ is the centre of the circle. If the diameter $AOB$ rotates about $O$, which of the following is/are constant?

I. $\theta+\phi$ II. $AC+BD$ III. $AC\times BD$

In the figure, $AB=16$, $CD=8$, $BF=9$, $GD=4$, $EG=2$. Find $GC$.

In the figure, $ABCD$ is a square of side $a$ and $BDEF$ is a rhombus. $CEF$ is a straight line. Find the length of the perpendicular from $B$ to $DE$.