In a triangle, two sides and the median to the third side have respective lengths 5, 13, and x. List all possible integer values of x.
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- There is an elegant solution/proof here! I found a far more complicated coordinate argument.
- Some students might make an educated guess based on insight but the real challenge is to explain one's conjecture!
- Challenge yourselves with this - if you see how to do it, suggest an approach but don't give it all away for at least a few hours!
- We generally think of these as only appropriate for our best and brightest but there's no harm in throwing it out to all of our geometry students- amazing things happen when we open up these kinds of problems to everyone!