Geometry ( ජ්‍යාමිතිය )

There was an Olympiad question of  evaluating the sum arccot(2) + arccot(3) by geometrical approach. My issue is how can you use only one figure to evaluate sum of infinite series of angles arccot(3) + arccot(7) + arccot(13)+….and show that ...

In general can you use the standard form y – β = m(x –  α)  of a straight line of gradient m , going through a point (α,β) in the case of finding equation of a tangent line drawn to ...