Two circles of radius 70 and 73 are placed on the x-axis, and both are tangent to each other. Then another circle is constructed so that it is tangent to the two larger circles and the x-axis. The original circles are labeled 0 and 1, and the new circle is labeled 2. Two new circles are constructed, one with tangency to 0, 2 and 2, 1. We continue this process ad infinum. The first set of circles is called the first layer, the second circle is Layer 1, etc. What is the sum of the radii to the -.5 from layer 1 to layer 7?
Hint: This is a lot of words, so draw out a diagram. Use right triangles to get a relationship between radii of different layers.
Level: 7
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