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Tag Archives: AIME
Conceptual Solution to 2008 AIME I, Problem 14
Here’s a solution to problem 14 on the 2008 AIME I contest that attempts to avoid computation as much as possible. Sometimes, it’s an amusing exercise to try to solve a contest problem entirely in your head. Doing so often forces … Continue reading
Posted in Contest Math, math
Tagged AIME, circles, ellipse, geometry, optimization, tangent
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2013 AIME 2 Problem 10
I’ve been asked about the following problem from the 2013 AIME 2 a few times, so I decided to blog a couple of solutions for it: Given a circle of radius , let A be a point at a distance from … Continue reading
2012 AIME 1 Problem #12
I was checking out Mess or Math?’s cool blog and her latest post wonders whether problem 12 on the 2012 AIME 1 has a simple solution. Simple is a subjective term. The problem’s setup certainly suggests invoking things like the … Continue reading
Barycentric Coordinates
Draw a triangle and add a point P somewhere on its boundary or in its interior. Next, connect P to each of the three vertices. The triangle will be split into 3 smaller triangles, possibly degenerate. Label the fraction of the area of … Continue reading