The circle shown in the diagram has, as tangents, the x-axis, the y-axis, the line x + y = 2 and

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The question is to determine the values k for which the line y is equal to x plus k is tangent t

The circle shown in the diagram has, as tangents, the x-axis, the y-axis, the line $x + y = 2$ and the line $x + y = 2k$, where $k > 1$. Find the value of $k$.