1999 年

In the figure, find the equation of the circle with $AB$ as a diameter.

The figure shows a circle centred at $C$ and passing through $O(0,0)$, $A(6,0)$ and $B(0,8)$. Which of the following must be true? I. $C$ lies on the line $\dfrac{x}{6}+\dfrac{y}{8}=1$. II. The radius of the circle is $10$. III. $OC$ is perpendicular to $AB$.

Two circles with equations $(x+1)^2+(y+1)^2=25$ and $(x-11)^2+(y-8)^2=100$ touch each other externally at a point $P$. Find the coordinates of $P$.

In the figure, $ABCD$ is a rectangle. $M$ is the midpoint of $BC$ and $AC$ intersects $MD$ at $N$. Area of $\Delta NCD$ : area of $ABMN=$