Crazy circles

Geometry Level 5

Three circles mutually tangent with centers \(A\), \(B\) and \(C\) have radii of \(21\), \(14\) and \(c\) respectively. Let the circle with center \(D\) and radius \(2\) be externally tangent to the three circles, and let the circle with center \(E\) and radius \(R\) be internally tangent to the three circles. Find \(\lfloor 100(c+R) \rfloor\).

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