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Category Archives: Contest Math
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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Do you believe this?
Here’s a triangle: I’ll use the vertex labels to also denote the corresponding angle measures. Take the sines of all 3 angles in the triangle: , , and . Would you believe it if I told you that these three … Continue reading
Posted in Contest Math, math
Tagged law of cosines, Ptolemy's theorem, similarity, sine, triangles, trigonometry
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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 Math Prize for Girls: #1620
Here are comments and solutions to (some of) the problems on the 2012 Math Prize for Girls contest that took place at MIT on September 22.
Use Your Mind to Save Yourself Time
I’m looking forward to Games Night at the Math Prize for Girls coming up this weekend. I’ve been working with the author of “Mess or Math?” to create a really fun math activity and I hope many of you who … Continue reading
Posted in Contest Math, math, Math Education
Tagged AMC 12, circles, circumference, geometry, similarity, tangent circles
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2011 Math Prize for Girls: #15
Here are comments and solutions to problems 15 on the 2011 Math Prize for Girls contest that took place at MIT on September 17, 2011. Earlier I blogged comments and solutions for problems 610, problems 1115, and problems 1620.
2011 Math Prize for Girls: #610
Here are comments and solutions to problems 610 on the 2011 Math Prize for Girls contest that took place at MIT on September 17, 2011. Earlier I blogged comments and solutions for problems 1115 and problems 1620.