ISL 1992
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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
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Re: ISL 1992
Hmm.Direct application of complex numbers.(Actually I talked with Zadid vaia about this problem in today's PMS class.)
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Re: ISL 1992
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।
Re: ISL 1992
My intuition says spiral similarity and perpendicular lemma should yield a solution (Though I am perfectly happy with the complex one )
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Nur Muhammad Shafiullah | Mahi
- FahimFerdous
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Re: ISL 1992
I guess a spiral similarity must work here. Working on it.
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