two tangent circles touching two lines
Source:
November 16, 2009
trigonometrygeometry
Problem Statement
The figure below shows two parallel lines, and , that are distance apart:
[asy]unitsize(7);
draw((-7, 0) -- (12, 0));
draw((-7, 12) -- (12, 12));
real r = 169 / 48;
draw(circle((0, r), r));
draw(circle((5, 12 - r), r));
pair A = (0, 0);
pair B = (5, 12);
dot(A);
dot(B);
label("", A, plain.S);
label("", B, plain.N);
label("", (12, 0), plain.E);
label("", (12, 12), plain.E);[/asy]
A circle is tangent to line at point . Another circle is tangent to line at point . The two circles are congruent and tangent to each other as shown. The distance between and is . What is the radius of each circle?