Tons of Triangles

Geometry Level 1

All points on a Cartesian plane are colored either red\color{#D61F06}{\text{red}} or blue\color{#3D99F6}{\text{blue}}.

For all positive numbers r,r, there exists a non-degenerate isosceles triangle with legs of length rr whose vertices are all colored __________\text{\_\_\_\_\_\_\_\_\_\_}.

Is the statement above true for at least one of the colors?

Note: A degenerate triangle is one where all three vertices lie on a straight line.


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