Question

若 $B$ 是以 $P$ 为圆心的圆 $C$ 上一点，则在圆 $C$ 所在平面内，所有满足“ $A$ 到 $B$ 的距离不大于 $A$ 到圆 $C$ 上任意其他点的距离”的点 $A$ 构成

If $B$ is a point on circle $C$ with center $P,$ then the set of all points $A$ in the plane of circle $C$ such that the distance between $A$ and $B$ is less than or equal to the distance between $A$ and any other point on circle $C$ is

从 $P$ 到 $B$ 的线段

the line segment from $P$ to $B$

以 $P$ 为端点并经过 $B$ 的射线

the ray beginning at $P$ and passing through $B$

一条以 $B$ 为端点的射线

a ray beginning at $B$

一个以 $P$ 为圆心的圆

a circle whose center is $P$

一个以 $B$ 为圆心的圆

a circle whose center is $B$

答案：B

知识点：圆极端原理

难度评级：1510

小提示：

当 $A\ne P$ 时，圆上离它最近的点位于从 $P$ 经过 $A$ 的射线上

For $A\ne P,$ the nearest point of the circle lies on the ray from $P$ through $A$

大提示：

要使这个径向最近点恰为给定的点 $B$

Require that this radial nearest point be the fixed point $B$

解答：

对于任意 $A\ne P$ ，圆上离 $A$ 最近的点是从 $P$ 经过 $A$ 的射线与圆的交点。仅当 $A$ 位于从 $P$ 经过 $B$ 的射线上时，该交点才是 $B$ 。圆心 $P$ 也符合条件，因为它到圆上各点的距离相等。因此所求轨迹就是这条射线。

因此，正确答案是 B。

For any $A\ne P,$ the closest point of the circle to $A$ is where the ray from $P$ through $A$ meets the circle. This point is $B$ exactly when $A$ lies on the ray from $P$ through $B.$ The center $P$ also qualifies because every point on the circle is equally distant from it. Thus the locus is that ray.

Therefore, the correct answer is B.

1978 AMC 12 第 10 题

答案：B

难度评级：1510

小提示：

大提示：

解答：

其他年份的第 10 题