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Algebra Difficulty 6.0 National Olympiad Prove it United Kingdom

The angles $A$ , $B$ and $C$ of a triangle are measured in degrees, and the lengths of the opposite sides are $a$ , $b$ and $c$ respectively. Prove that
$60 \le \frac{aA + bB + cC}{a+b+c} < 90.$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; question papers published free at bmos.ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.