Here is new one in the series of horrible problems- Q.In a triangle ABC, with angle ABC=(60-x) degree and angle ACB=30 degree.Point P is taken such that BP=CP and angle PBC=x degree.Find angle BAP.
Sometimes I fear am I repeating the problems?If some one find it to be so, please inform. Other than this, if some one have found these type of problems or solutions , in any book or anywhere, then please do inform me.I don't want to waste my time in reinventing the wheel.As far as my knowledge goes, other than 3 or 4 problems , rest are original.I used common tehnique in proving every problem, that works in every problem.If I include trigonometrical solutions, than these problems are not more than trivial.But any response is encouraging let that be Narsimhan's 2 line solution. Again , big question remain unanswered, what is PURE GEOMETRICAL SOLUTION. If with some definition , we can exclude trigonometrical solution, then we can see some wonderful mathematics.In mathematical gazette , C. Tripp had conjecturd that pure geometrical solution is possible, whenever all angles are ratinal multiples of pi. But he had mentioned he is far from proving it.But I don't know , what is geometrical solution?How you can differentiate trigonometrical solution from geometrical solution?I was encouraged , when I knew that I have at least 5 or 6 readers. Initially I thought, there are only 2 or 3 readers. I hope , I am making sense whatever I am writing.This time I am expecting some fruitful response. Though responses are very few, which is little bit discouraging.Philippes's reponse was most encouraging.