One more boring geometry problem
Sujeet Kumar
Q.In a triangle ABC , point P is taken so that ,angle ABP=20 degree, angle PBC=60 degree,angle PCB=40 degree and angle PCA=30 degree.Find angle BAP.
When I(I think this is true for every one else) first started studying geometry , I encountered the problems which had nice angles such as 30, 45, 60 and 90 degrees.We had also exercises of construction of these angles.That time we had no idea of non-constructibles exercises or what is meaning of nonconstructible.I knew about Golden ratio much later, again this was related to 36 degree , which is again constructible.In fact , for me Langley Problem was first problem of its kind where angles such as 20 degree was used.I think this discrimination was because of nonconstructible nature of
20 degree.But, nonconstructible angles need not be uninteresting.Certainly nature doesn't discriminate
against them.
Here is a funny property of 10 degree.But , I knew this from a unreliable source, so I don't claim it to be 100% true.
Most of us must have tried skidding of stone on still surface of water.Stone skid maximum when thrown at 10 degree on the surface of water.I think skid is right word or we can say jumping of the stone.