I was browsing through my past photos and dug up an ample amount of geometry proof problems I've solved in the past. Starting today, I will select and share one of those problems and post it on here every few days. I hope you guys will find these problems interesting and fun.
This one caught my eye as the first problem:
\(ABC\) is a right triangle at \(B\). \(D\) is a point inside \(ABC\) such that \(AD=AB\). \(E\) is on \(AC\) satisfying \(DE\perp BD\). Suppose cirucmcircle \((CDE)\) intersects \(BC\) at \(F\). Prove that \(BE=EF\).
Looking forward to solutions.involving different methods. Exercise your creativity on the limitless space of geo.