# 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, 9 months ago

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