2019 AMC 8 Problem 24
Attempt Problem 24 of the 2019 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
In triangle point divides side so that Let be the midpoint of and let be the point of intersection of line and line Given that the area of is what is the area of
Answer: B
Small hint:
Use area ratios from bases on the same line
Big hint:
Let and use
Video solution:
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Written solution:
Since triangles and have areas in the ratio Thus and
Because is the midpoint of triangles and each have area Let Then as well, since and both triangles have their third vertex on line
Segment splits so Also, and have bases and on the same line, so their areas are in the ratio
Therefore Solving gives so
Thus, the correct answer is B.
Problem 24 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
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- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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