1991 AMC 12 第 29 题
先试着解答 1991 AMC 12 第 29 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 1991 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。
29.
等边三角形 经过压折，使顶点 落到点 ，该点位于 上，如图所示。若 且 ，则折痕 的长度为
Equilateral triangle has been creased and folded so that vertex now rests at on as shown. If and then the length of crease is
小提示：
折痕是一个点及其折叠后对应点所连线段的垂直平分线
A fold crease is the perpendicular bisector of the segment joining a point to its image
大提示：
设 、、、
Place and
解答：
使用提示中的坐标，点 的垂直平分线条件为 ，化简得 该直线与 相交于 ，与 相交于 。因此
因此正确答案为 B。
With the coordinates in the hint, the perpendicular-bisector condition for is which simplifies to Intersecting this line with gives Intersecting it with gives Hence
Thus the correct answer is B.
其他年份的第 29 题
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 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
- 1992 AMC 12
- 1993 AMC 12
- 1994 AMC 12
- 1995 AMC 12
- 1996 AMC 12
- 1997 AMC 12
- 1998 AMC 12
- 1999 AMC 12