I had recently opened a discussion thread about a geometry problem from an online-math-camp-test after the test was over. However, it turns out I broke some rule. There was a 24-hour rule ("no problems are to be discussed until 24 hours have passed") and I somehow missed that rule. Now that 24 hours have passed, it's completely okay to discuss about that problem.
I've deleted the previous discussion thread and I'm really sorry for the inconvenience.
Here's the problem I was talking about:
\(2∠X=3∠Y\) and \(YZ=x\), \(XZ=y\), \(XY=z\). Find a triangle that has positive integer side lengths and satisfies the equation:
Good luck and thanks in advance!
Problem source: RGS Math Olympiad-June 2013.
This problem was also recycled in BdMO online math camp exam-1.