If the lines joining corresponding points of two directly similar figures are divided proportionally, then the locus of the points of the division will be a figure directly similar to the given figures.
Douglas-Neumann Theorem
See also
Directly Similar, Petr-Neumann-Douglas TheoremExplore with Wolfram|Alpha
References
Eves, H. "Solution to Problem E521." Amer. Math. Monthly 50, 64, 1943.Musselman, J. R. "Problem E521." Amer. Math. Monthly 49, 335, 1942.Referenced on Wolfram|Alpha
Douglas-Neumann TheoremCite this as:
Weisstein, Eric W. "Douglas-Neumann Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Douglas-NeumannTheorem.html