ISL 1992

[shehab ahmed]

A convex quadrilateral $ABCD$ is such that its two diagonals are equal.Equilateral triangles are constructed on the sides of the quadrangle and outside.Let, $P,Q,R,S$ be the centres of the triangles constructed on $AB,BC,CD,DA$ respectively.Prove that $PR$ is perpendicular to $QS$.

[Phlembac Adib Hasan]

Hmm.Direct application of complex numbers.(Actually I talked with Zadid vaia about this problem in today's PMS class.)

[shehab ahmed]

এভাবে বলা উচিত নয়।তোমার কথা শুনে মানুষ ভাবতে পারে জটিল সংখ্যা আর কোনোভাবে এটা সল্ভ করা যায় না।কিন্তু হয়ত এটার অন্য কোনো সমাধানও আছে।

[*Mahi*]

My intuition says spiral similarity and perpendicular lemma should yield a solution (Though I am perfectly happy with the complex one )

[FahimFerdous]

I guess a spiral similarity must work here. Working on it.