Geometric Series of Circles

Geometry Level 4

The central circle in the figure attached, is of radius \( 10 \) units. Two tangents are drawn to that circle from Point A, such that the angle between the two tangents equals \( 20^{\circ} \). This is mirrored on the other side of the central circle.

Next, an infinite sequence of circle is generated on both sides, such that each circle is tangent to the previous circle and the two tangent lines, on its side, as depicted in the figure.

Find the total area of all the circles, correct to two decimal places.

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