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.