1954 AMC 12 第 26 题
先试着解答 1954 AMC 12 第 26 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1954 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
26.
点 将直线段 分割，使得 。分别以 和 为直径作圆，两圆的一条公切线与 的延长线交于 。则 等于：
The straight line is divided at so that Circles are described on and as diameters and a common tangent meets produced at Then equals:
较小圆的直径
the diameter of the smaller circle
较小圆的半径
the radius of the smaller circle
较大圆的半径
the radius of the larger circle
两圆半径之差
the difference of the two radii
小提示：
点 是两圆的外位似中心
The point is the external center of similitude of the two circles
大提示：
设 ，并按 比较 到两圆心的距离
Let and compare the distances from to the two centers in the ratio
解答：
设 ，则 ，且 。从 起量，两圆心的位置分别为 和 ，两半径之比为 。若 ，公切线使 成为两圆的外位似中心，所以 因此 ，且 这正是较小圆的半径。
因此，正确答案是 B。
Let so and Measured from the circle centers are at and and their radii are in the ratio If the common external tangent makes the external center of similitude, so Hence and which is the radius of the smaller circle.
Thus, the correct answer is B.
其他年份的第 26 题
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
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- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
- 1966 AMC 12
- 1967 AMC 12
- 1968 AMC 12
- 1969 AMC 12
- 1970 AMC 12
- 1971 AMC 12
- 1972 AMC 12
- 1973 AMC 12
- 1974 AMC 12
- 1975 AMC 12
- 1976 AMC 12
- 1977 AMC 12
- 1978 AMC 12
- 1979 AMC 12
- 1980 AMC 12
- 1981 AMC 12
- 1982 AMC 12
- 1983 AMC 12
- 1984 AMC 12
- 1985 AMC 12
- 1986 AMC 12
- 1987 AMC 12
- 1988 AMC 12
- 1989 AMC 12
- 1990 AMC 12
- 1991 AMC 12
- 1992 AMC 12
- 1993 AMC 12
- 1994 AMC 12
- 1995 AMC 12
- 1996 AMC 12
- 1997 AMC 12
- 1998 AMC 12
- 1999 AMC 12