2002 年

In the figure, $EAF$ is a common tangent to the circles at the point $A$. Chords $AC$ and $BC$ of the smaller circle are produced to meet the larger circle at $G$ and $D$ respectively. Which of the following must be true? I. $\angle ADG=\angle EAG$ II. $\angle ABD=\angle AGD$ III. $\angle BAE=\angle ADB$

In the figure, $x=0$, $y-a=0$ and $y+a=0$ are tangents to the circle. The equation of the circle is

The equation of a circle is given by $(x-a)^2+(y+b)^2=a^2+b^2$, where $a>0$ and $b>0$. Which of the following must be true? I. The centre of the circle is $(a,-b)$. II. The circle passes through the origin. III. The circle cuts the $x$-axis at two distinct points.

The standard deviation of the four numbers $m-7$, $m-1$, $m+1$ and $m+7$ is