1995 AMC 12 Problem 9
Attempt Problem 9 of the 1995 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. The total number of triangles of any size in the figure is
Answer: D
Small hint:
Separate the triangles by size before counting
Big hint:
Count one orientation and use the square’s rotational symmetry
Solution:
There are smallest triangles, each bounded by a half-side, a half-diagonal, and a half-midline. There are triangles whose base is a full side and vertex is the center, and half-square triangles cut off by a diagonal. The total is Thus the correct answer is D.
Problem 9 in other years
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