Problem of the Week from Harvard MIT Math Tournament!

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#math #olympiad #geometry

Three smaller circles are placed in a grid and a larger one is tangent to them. What is the radius of the large circle? This is one of the past problems from the Harvard MIT math tournament (HMMT) problem of the week.

0:00: Introduction
0:23: Geometry problem
0:43 The boring solution
1:23 The fancy solution

  1. Dedekind cuts
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Do check out the current problem of the week, which ends in less than 12 hours!
Also, never mind my random flashback on orbital :p

dedekindcuts
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Interesting. Before clicking your thumbnail, I would have bisected AB and BC (or AC) and drawn perpendicular slopes from their midpoints. Those two slopes intercepts a point which is precisely the centre of a circle. From there, a radius could be worked out. Your way is shorter cut.

pinklady