In △ABC, let D∈CA and E∈AB such that ∠ABD=∠CBD and ∠ACE=∠BCE. A rhombus is inscribed into the quadrilateral BCDE (that is, the vertices of the rhombus lie on distinct sides of BCDE). Let ϕ be the non obtuse angle of the rhombus. Prove that, ϕ≤max(∠ABC,∠ACB).
#Geometry
#Inequalities
#Angles
#Quadrilaterals
#Rhombus
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