# Classical geometry 2

Geometry Level 4

In the figure to the right, the yellow circle is tangent to $$\triangle ABC$$ at points $$D, E, F.$$

$$2 \sqrt{14}, 4 \sqrt{3},$$ 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 the yellow circle?

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