2015 Countdown Problem #18: A Vicious Circle

Geometry Level 4

A circle of diameter 2015 cm has one vertical and one horizontal line, both initially intersecting at the centre of the circle.

The horizontal line is shifted upwards by 20 cm and the vertical line is shifted rightwards by 15 cm.

For each subsequent time, the horizontal line is shifted upwards by \(\frac{1}{3}\) the previous distance it shifted, and the vertical line is shifted rightwards by \(\frac{1}{3}\) the previous distance it shifted. This process repeats indefinitely.

The end result is shown in the image. Find the difference between the shaded and unshaded areas.

This problem is part of the set 2015 Countdown Problems.

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