Funky Star

Geometry Level 4

Find the measure of the star's internal angle at the point indicated.

The radius of the small circle is 1. The large circle has a center on the small circle and its radius is 3. The vertices of the shortest and the longest arms of the star are on the line connecting the centers of the circles. The lines going to those points and to the point indicated by the arrow are tangent to the small circle. The star may not, in the end, connect quite as prettily as shown, but the above facts are sufficient to find the angle.

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