SOLUTION: Can you give me a couple of tough proofs to study from for my exam tomorrow? or a link to a good website

Question 386579: Can you give me a couple of tough proofs to study from for my exam tomorrow? or a link to a good website
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Here is a nice geometry proof question:

ABC is a triangle with angle A = 90. Points D and E lie on sides AC and AB, respectively, such that angle ABD = angle DBC and angle ACE = angle ECB. Segments BD and CE meet at I. Determine whether or not it is possible for segments AB, AC, BI, ID, CI, and IE to all have integer side lengths (2010 USAMO, #1).

There are probably multiple ways to solve this; my solution during the actual exam involved a little trigonometry. I encourage you to go for it and challenge yourself!
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