Similarity points
- Author:
- Ryan Hirst
E is the external similarity point of the two circles.
K is the internal similiarity point.
Notes:
- Given d, r and s the ratio a/(d+a) = r/s gives a unique solution, but it is an incomplete question. a appears in the numerator and denominator in such a way that, if we change the sign of a, the sign of a/(d+a) does not change. To find a solution on the same side of B, but on the other side of A, we must ask explicitily: a'(d-a') =? r/s There is such an a'.
- solving for a' in terms of a and d, we get a' = ad/(2a + d) where a', a and d are all positive values (lengths). This gives the range restrictions: a>a' d> 2a' Assume A is the smaller circle. Then these conditions are the same thing as saying -both intersections lie on the same side of B as A - E is on the far side of A, -K falls between A and B, and is closer to A. These may or may not already be obvious, depending on how you frame the problem.