# 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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