Date: Thu, 2 Apr 1998 11:56:20 -0600 (CST) From: Dave Rusin To: ck6@evansville.edu Subject: Re: spelling >spelling of Apollonius Oopsie! Thanks. >construction of a circle tangent to two given lines and a circle? A circle of radius R which is tangent to two lines has its center a distance R from each line; in particular, the center must lie on the bisectors of the angles between those lines. If this circle is also tangent to a circle of radius r then the distance between the centers has to be | R +- r |, that is, it's more/less than the distance to the given center by exactly r. You can say it differently: take that angle bisector and translate perpendicularly by a distance r to get a new line. Then this new line's distance from the desired center will have to equal to given center's distance from the desired center. Aha! Now we recognize the description of a parabola. So the center of the desired circle is on the intersection of a parabola and a line (actually one of several parabolae/lines). Given the center, of course, the radius R is determined by the tangency to the given circle. dave