MathDB

Let

r > 0

be a real number. All the interior points of the disc

D(r)

of radius

r

are colored with one of two colors, red or blue.
[*]If

r > \frac{\pi}{\sqrt{3}}

, show that we can find two points

A

and

B

in the interior of the disc such that

AB = \pi

and

A,B

have the same color [*]Does the conclusion in (a) hold if

r > \frac{\pi}{2}

? Proposed by S Muralidharan

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