Classical geometry 2

Geometry Level 4

In the figure above, the yellow circle is tangent to the sides of \( \triangle ABC \) at \( D \), \( E \) and \( F \). If \( 2 \sqrt{14} \), \( 4 \sqrt{3} \) and \( \sqrt{42} \) are the lengths of the common tangents to the semicircles of diameters \((BD, CD), (CE, AE)\) and \((AF, BF),\) respectively, what is the radius of yellow circle?

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