1996 年

In the figure, $ABCD$ is a trapezium with $AB\parallel DC$. $AH$ bisects $\angle BAD$ and $DH$ bisects $\angle ADC$. Which of the following must be true?

I. $\angle AHD=90^\circ$ II. $\angle ADC=\angle BCD$ III. $\angle BAD+\angle BCD=180^\circ$

In the figure, $DE:EF=$

$A(-3,2)$ and $B(1,3)$ are two points. $C$ is a point on the $AB$ produced such that $AB:BC=1:2$. Find the coordinates of $C$.

$C_1: x^2+y^2=4$ and $C_2: x^2+y^2=9$ are two circles. A chord $AB$ of $C_2$ touches $C_1$. Find the length of $AB$.