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magneto1
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(BMO, 2013) The angles $A$, $B$, $C$ of a triangle are measures in degrees, and the lengths of the opposite sides are
$a$,$b$,$c$ respectively. Prove:
\[
60^\circ \leq \frac{aA + bB + cC}{a + b + c} < 90^\circ.
\]
Edit: Update to include the degree symbol for clarification. Thanks, anemone.
$a$,$b$,$c$ respectively. Prove:
\[
60^\circ \leq \frac{aA + bB + cC}{a + b + c} < 90^\circ.
\]
Edit: Update to include the degree symbol for clarification. Thanks, anemone.
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