Enneagram Incircle

Geometry Level pending

An enneagram constructed from the vertices of a regular nonagon is inscribed in the unit circle. Inside the enneagram, a blue incircle is drawn within a kite, as shown in the figure. If the radius of this circle is expressed as A B B sin π C \dfrac{A}{B} - B\sin\dfrac{\pi}{C} , submit A + B + C A+B+C .


The answer is 21.

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