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The clouds finally cleared up out here in time to see the partial eclipse. I used a pinhole (more precisely, pen-hole) to project an image.

Reports were that the sun was about 75% obscured. Here's the problem:

Given: two circles, A and B, the same size, with A in front of B.

When the two centers coincide, B is 100% obscured by A.
When the two circles are tangent (each center coincides with the other circle's circumference), B is 0% obscured.

In doing the sort-of-complicated calculations that tell how the moon passes in front of the sun, it seems reasonable that the first number they come up with is the relative positions of the sun and moon: how much overlap there is. For example, the moon's center will be 3/4 of the distance from the sun's center to its edge. (This would be a lot easier with pictures.)

Fortunately for astronomers and eclipse-chasers, the sun and the moon have almost identical diameters, as seen from Earth.

Here's the problem:

Part 1:
Circle A covers part of circle B. If the center of A is on the circumference of B, how much of B is covered by A? (The symmetrical question is, how much of B is visible? I don't know which would be easier.)

Part 2:
The center of A is somewhere along a radius of B. Let the radius be 1, and let the center of A be at 2/3 of the radius of B. How much of B is covered (or visible)?

Is there a general formula that gives B-%-hidden vs position-of-A-center-along B's radius?

I started to work this one (Part 1) sometime last year, but I don't remember how far I got.
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