In a triangle
, let
and
be the feet of the angle bisectors of angles
and
, respectively. A rhombus is inscribed into the quadrilateral
(all vertices of the rhombus lie on different sides of
). Let
be the non-obtuse angle of the rhombus. Prove that
.
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In a triangle $ABC$, let $D$ and $E$ be the feet of the angle bisectors of angles $A$ and $B$, respectively. A rhombus is inscribed into the quadrilateral $AEDB$ (all vertices of the rhombus lie on different sides of $AEDB$). Let $\phi$ be the non-obtuse angle of the rhombus. Prove that $\phi \leq \operatorname{max}\{ \angle BAC, \angle ABC \}$.
Školjka