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## Orthogonality

Let ABC be a triangle and D be the midpoint of BC. Suppose the angle bisector of $$\angle ADC$$ is tangent to the circumcircle of triangle ABD at D. Prove that $$\angle A = 90^o$$ . (Regional Mathematics Olympiad, India, 2016)

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## Some Beautiful Books

Straight Lines and Curves by Vasiliyev N. B. Vasilyev was the chief architect of Mathematical Olympiads in Soviet Union. This gem from erstwhile Soviet Union’s publication, explores loci of points in plane and space. The entire discussion is aided by geometric intuition. The authors occasionally use algebraic tools to augment the ideas. The holistic nature […]

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## Shrinking the diameter of Vitali Set

Claim: The diameter of Vitali Set V on [0, 1] can be shrinked as much as we please Proof:  Let R be an equivalence relation defined on [0,1] such that x is related to y if x – y is rational. Let E be an equivalence class corresponding to the equivalence relation R. In order to […]