Triangle Inequality

inspired by a visual from spring-of-mathematics, I was curious about making it dynamic. I'm not sure the parallelograms help, but as I was making, I had the mild surprise of the circles intersecting on the third side, but then realized that that point had to be the foot of the altitude. Lovely how perfect triangles are! So what do you think, does this visual (or the more elegant original) help? Original image: http://spring-of-mathematics.tumblr.com/post/128963388229/triangle-inequality-theorem
More GeoGebra at bit.ly/mh-ggb