Difference between revisions of "2008 Mock ARML 1 Problems/Problem 3"
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Revision as of 17:33, 29 May 2008
Problem
In regular hexagon with side length , intersects at , and intersects at . Compute the length of .
Solution
Let be the foot of the perpendicular from to . Since is an inscribed angle with measure , it follows that is a , and and . Also, . Note that by ratio . Thus .
By the Pythagorean Theorem, . Thus .
See also
2008 Mock ARML 1 (Problems, Source) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 |