On May 3, 12:59*pm, Tim Wescott wrote:
Consider two circles, of arbitrary diameter, and a point, all on a plane.

I want to inscribe an arc that is tangent to both circles, and which
passes through the point.

Anyone know a way to construct the arc? *I'm not snickering in the
background here as I pose puzzles -- this is a drafting problem that I'm
running into quite a lot lately.

--

Tim Wescott
Wescott Design Serviceshttp://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details athttp://www.wescottdesign.com/actfes/actfes.html

My approch:

One assues three circles. C1, C2 and Carc

which can be defined by x1,y1, R1 x2,y2,R2 and xa,ya,Ra
Carc is the curve you are looking for

a tanjent unit vector on each circule is defiend as ((2(x-xn)x) i
+(2(y-Yn)y )j)/(Sqrt( ((2(x-xn))^2 +(2(y-Yn)y)^2) where i and j are
unit vectors in the x and y direction

A tanjent condition is acheved when the C1, Carc share the same point
and tanjent vectors are colinear. Plug the equations into Mathmaica
and pray