Math: Triangle abc is a right triangle (c being 90 deg). the altitude intersects the hypotenuse at D.?

Name ALL geometric means present and plz explain

Math: Triangle abc is a right triangle (c being 90 deg). the altitude intersects the hypotenuse at D.?
Triangles ABC, ACD, and CBD are all similar triangles, meaning their corresponding angles are congruent. (This is probably a theorem in your geometry book, but it's fairly easy to prove. To show that triangles ABC and ACD are similar, just observe that each one contains a right angle and each one contains angle A. Since the measures of the angles in a triangle always add up to the same thing, namely 180 degrees, that means the remaining angles in those triangles must also have the same measures. The proof that ABC and CBD are similar triangles is, well, similar.)


Because triangle ACD is similar to triangle CBD, we have AD/CD = CD/DB (where AD means the measure of line segment AD, etc.). Cross-multiplying, we have (CD)^2 = (AD)(DB); in other words, CD is the geometric mean of AD and DB.


I don't think there are other geometric means in there, at least not without adding more points and line segments, but maybe there's something I'm not seeing.