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Australian Intermediate Mathematics Olympiad 2015 Question 2

AIMO AUSTRALIA · Australian Intermediate Mathematics Olympiad 2015

Question 2

A circle is inscribed in a hexagon $ABCDEF$ so that each side of the hexagon is tangent to the circle. Find the perimeter of the hexagon if $AB=6$, $CD=7$, and $EF=8$.

Numerical answer only; a non-negative integer less than 1000.