Difference between revisions of "2005 Alabama ARML TST Problems/Problem 9"
(New page: ==Problem== A square is inscribed in a circle of diameter 12. Two vertices of a triangle are also vertices of one side of the square. The other vertex of the triangle is on the circle. Fin...) |
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Latest revision as of 23:19, 3 March 2008
Problem
A square is inscribed in a circle of diameter 12. Two vertices of a triangle are also vertices of one side of the square. The other vertex of the triangle is on the circle. Find the largest possible area of the triangle.
Solution
Let the "base" of the triangle, which is a side of the square, be 
, and let the third point of the triangle be 
. Clearly we want to be as far as possible from , so we have that the base of the triangle is 
and the height, after some side chasing, is 
. We multiply and divide by 2 to get 
.
See also
| 2005 Alabama ARML TST (Problems) | ||
| Preceded by: Problem 8 |
Followed by: Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
