Can You Solve This Fiendishly Brilliant Math Puzzle?

The geometry puzzle designed by @panbtc. Image Credit: C.Carpinet/IFLScience

There is nothing quite like a tricky math puzzle to blow some of the cobwebs out of our heads. This one designed by Twitter user @panbtc manages to combine a simple setup, a tricky approach, and an “of course it is” solution in this brilliant little puzzle.

You are looking for the width of the rectangle. You know that the length of the shorter side is 8 and there are two circles inscribed in it. These circles are tangent, meaning that they touch on one point. A segment of a line, parallel to the shorter side of the rectangle, goes through this tangent point. The length of this segment is 6.

So how long is the longer side?

It might not look like it but you have everything you need to solve it.

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Hints if you are stuck

OK, here are just a few hints if you are stuck. First of all, the size of the circles doesn’t matter to solve this puzzle.

You should remember that the segment is made of two chords. If you have a perpendicular line that cuts a chord in two it will go through the center. And finally, if two circles are tangent, their centers and the tangent point belong to the same line.

Now, go, be mathematical and keep an eye out for a certain notorious triangle…

If you want the full solution Presh Talwalkar at MindYourDecision has got you covered and you can check it out here.


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