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Geometry 1

In \(\triangle ABC\), let \(D\in CA\) and \(E\in AB\) such that \(\angle ABD=\angle CBD\) and \(\angle ACE=\angle BCE\). A rhombus is inscribed into the quadrilateral \(BCDE\) (that is, the vertices of the rhombus lie on distinct sides of \(BCDE\)). Let \(\phi\) be the non obtuse angle of the rhombus. Prove that, \(\phi\le \max(\angle ABC,\angle ACB)\).

This problem belongs to the set TST Bangladesh 2014 Problems.

Note by Jubayer Nirjhor
3 years, 6 months ago

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