AMC 8 2005 Problem 21
AMC8 2005 年第 21 题
排列与组合★★★☆☆
How many distinct triangles can be drawn using three of the dots below as vertices?
使用下图中其中 3 个点作为顶点，可以构成多少个不重叠的三角形？
- A.9
- B.12
- C.18
- D.20
- E.24
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
The number of ways to choose three points to make a triangle is . However, two* of these are a straight line so we subtract 2 to get 18.
Case 1: One vertex is on the top 3 points Here, there is ways to choose the vertex on the top and ways the choose the 2 on the bottom, so there is triangles. Case 2: One vertex is on the bottom 3 points By symmetry, there is 9 triangles. Otherwise, the triangle is degenerate. Our final answer is
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