Construction of harmonic mean with ruler and compass

Question

Exercise 8.10 at this site http://www.euclidea.xyz/ claims that harmonic mean can be built with just 4 simple objects (lines and/or circles)

My best result is 6 objects (including perpendiculars and segment bisector). Do you have any hint to simplify the construction?

As the page is not accessible if you have not done all the previous ones, here is a screenshot of the page

Answer 1

Construct a isosceles triangle with base $b$ and the other two sides as $a+b$ each. Draw a circle of length a from the top vertex. Join the two points where it intersects the triangle. That length is half the harmonic mean. Double that length with a simple compass operation. Use similarity to prove the result.

Answer 2

$$H_\left(a,b\right) = \frac{2ab}{a+b} \Rightarrow \frac{H}{b} = \frac{2a}{a+b}$$

Mildly obfuscated solution illustrated here:

As you can see, this solution will get you a 4L/7E score. Getting 4/4 is a little tricker. :D