Difference between revisions of "2001 AMC 12 Problems/Problem 24"
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Revision as of 21:05, 3 July 2013
Problem
In ,
. Point
is on
so that
and
. Find
.
Solution
We start with the observation that , and
.
We can draw the height from
onto
. In the triangle
, we have
. Hence
.
By the definition of , we also have
, therefore
. This means that the triangle
is isosceles, and as
, we must have
.
Then we compute , thus
and the triangle
is isosceles as well. Hence
.
Now we can note that , hence also the triangle
is isosceles and we have
.
Combining the previous two observations we get that , and as
, this means that
.
Finally, we get .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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