2003 AIME II Problems/Problem 6
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Problem
In triangle
and point
is the intersection of the medians. Points
and
are the images of
and
respectively, after a
rotation about
What is the area if the union of the two regions enclosed by the triangles
and
Solution
Since a triangle is a
triangle and a
triangle "glued" together on the
side,
.
There are six points of intersection between and
. Connect each of these points to
.
There are smaller congruent triangles which make up the desired area. Also,
is made up of
of such triangles.
Therefore,
.
See also
2003 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |