Question

If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.

Answer 1

By the property of a circumscribed circle, the tangents drawn from an external point are equal. Thus:
$AB + BC + CD + DE + EF + FA = 2 \times \text {Perimeter of Hexagon.}$
Rearranging:
$AB + CD + EF = BC + DE + FA.$
Correct Answer: Proved