A classic Japanese geometry problem from 1820 (江戸時代の幾何学問題)

In this video, I discuss how to solve this classic Japanese sangaku (算額) geometry problem from 1820. For more information about sangaku problems, you can consult: https://www.ndl.go.jp/math/e/s1/c5.html In this problem, three circles with different radii are tangent to each other and rest tangent to a horizontal line. Given these constraints, if we know any two radii, can we determine the third? Better yet, can we find a relationship between the three radii? Spoiler: We can utilize the Pythagorean theorem and the basic axioms of planar geometry to find the answer.