Legendary Four Circles

Geometry Level 5

Circles \(k_1, k_2,\) and \(k_3\) are tangent pairwise, and each is tangent to a line \(l\). A fourth circle \(k\) is tangent to \(k_1, k_2, k_3\), so that \(k\) and \(l\) do not intersect. Find the distance \(d\) from the center of \(k\) to \(l\) if the radius of \(k\) equals 1.

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