Question:
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
Updated On: Dec 12, 2024
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Solution and Explanation
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
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