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.

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.

I solved it using the following steps:

ReplyDelete1) 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.

Your method definitely works. A simplier approach may be"

ReplyDelete1. 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