2006 AMC 8 Problem 19
Attempt Problem 19 of the 2006 AMC 8 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 2006 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Triangle is an isosceles triangle with Point is the midpoint of both and and is units long. Triangle is congruent to triangle What is the length of
Answer: D
Small hint:
Use the congruent triangles to relate and .
Big hint:
Then use and the fact that is the midpoint of .
Solution:
By the congruency condition, we know that
Also from the isosceles condition, we know that
Since is the midpoint of we know that
Thus, D is the correct answer.
Problem 19 in other years
- 1985 AMC 8
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