Tons of Triangles

Geometry Level 1

All points on a Cartesian plane are colored either \(\color{red}{\text{red}}\) or \(\color{blue}{\text{blue}}\).

For all positive numbers \(r,\) there exists a non-degenerate isosceles triangle with legs of length \(r\) 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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