I am having trouble finding a way to construct a circle, (circle A) which is tangent to two intersecting lines, and to two other circles, (circles B1 and B2) which are of equal radii, and each of which are tangent to the other, and to one of the lines.
Another way to express this problem is:
Given: two intersecting lines, with a third line bisecting the angle formed between them. Two circles of equal radius are tangent to each other at the bisector, and are each tangent to one of the two lines.
Construct a circle tangent to the two lines and the two circles.
I have tried this using, arbitrarily, two lines intersecting at 90 degrees, and then roughing in a drawing of the solution, and representing lengths with x's, y's, a's and b's, and trying to solve it algebraically.
I run into quadratic equations that are not reducible to something that can be constructed with compass and straight edge.
Any help?
Staroid
Another way to express this problem is:
Given: two intersecting lines, with a third line bisecting the angle formed between them. Two circles of equal radius are tangent to each other at the bisector, and are each tangent to one of the two lines.
Construct a circle tangent to the two lines and the two circles.
I have tried this using, arbitrarily, two lines intersecting at 90 degrees, and then roughing in a drawing of the solution, and representing lengths with x's, y's, a's and b's, and trying to solve it algebraically.
I run into quadratic equations that are not reducible to something that can be constructed with compass and straight edge.
Any help?
Staroid