## Wednesday, January 20, 2010

### Fox 231

Another simple claim.

1. I solved it using the following steps:
1) Found equation for tangent line for 2 arbitrarily placed semi-circles.
2) Then I compared the equation for 2 tangent lines between 2 different semi circles and they had the same slope, so that line had to be tangent to all three semi-circles.

Found the equation for the tangemt line by drawing a triangle in each semi-circle from the center to the tangent point and then vetically down then horizonally back to the center. These 2 triangle are similar and thus their sides are direct ratios. Math was not too heavy but way more than I can post in this blog.

2. Your method definitely works. A simplier approach may be"
1. Draw radiuses from A and B to the tangent points. (Let radius be a and b resp'ly.)
2. Draw a perpendicular line segment from the center of Red to the tangent line (call it x).
3. All 3 line segments are parallel.
4. Compute x in terms of a and b
5. If x = (a+b)/2 => m is their common tangent line.

-binary