Here is an extra ordinary geometry problem- Q.In a triangle ABC, point P is taken so that angle ABP=50 degree, angle PBC=30 , angle PCB=10 degree and angle PCA=50 degree.Find angle BAP.
If some one don't consider it as standard or serious mathemtics, they can take it as normal puzzles.As for my satisfaction, I saw the meaning of PUZZLE in the Consise Oxford English Dictionary. There one of meaning of puzzle is ?a game , toy, or problem designed to test ingenuity or knowledge?. As my english is not very good I saw the meaning of INGENUITY , its meaning is? the quality of being ingenious? and meaning of INGENIOUS is ?clever, original and inventive?.I think these problems satisfy all these condition, so these can considered as good puzzles.Going further I saw the meaning of PROBLEM , its meaning in mathematical sense is ?an inquiry starting from given conditions to investigate or demonstrate something?.Here these problems are investigating and demonstrating the beautiful inter- relationship between specific triangles and circle. So it is not wothless thing to devote some time to these problems , even if very easy solution can be given by other methods.Certainly these things are not going to find any practical application, but mathematics is not done for its practicality but for its beauty, fun , joy and feeling of triumph after one is able to find an elegant solution of a given problem.I think G. H. Hardy was of this opinion that it makes mathematician sick if his work find some practical use.But again life is miraculous thing when Hardy was writing this Number Theory had no use. Regards Sujeet