2011 AMC 12A Problems/Problem 13
Contents
Problem
Triangle has side-lengths
and
The line through the incenter of
parallel to
intersects
at
and $\overbar{AC}$ (Error compiling LaTeX. Unknown error_msg) at
What is the perimeter of
Solution
Solution 1
Let be the incenter. Because
and
is the angle bisector, we have
It then follows due to alternate interior angles and base angles of isosceles triangles that . Similarly,
. The perimeter of
then becomes
See also
2011 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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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