The circumference of a circle is colored with red and blue ink such that 2/3 of the circumference is red and 1/3 is blue. Prove that no matter how complicated the coloring scheme is, there is a way to...

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The circumference of a circle is colored with red and blue ink such that 2/3 of the circumference is red and 1/3 is blue. Prove that no matter how complicated the coloring scheme is, there is a way to inscribe a square in the circle such that at least three of the four corners of the square touch red ink.




Answered Same DayDec 25, 2021

Answer To: The circumference of a circle is colored with red and blue ink such that 2/3 of the circumference is...

Robert answered on Dec 25 2021
127 Votes
If R is the radius of the circle , the circumference of the circle is equal to 2πR. = π D
Let a square of side a is enclosed inside the circle such that all the four corners
of the square touch the circumference of the circle.
side of the square = a and diagonal =√ = √ * a
...
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