Not yet all read above but here my solution as usual very rustic brute force by "hand" but...i obtain the solution! :)
Circle by 3 points and big zoom for draw some tests :) Maybe 20! :)
AB = hypothenuse of a rectangle triangle 1*1 * hypo

I found the solution with 0.1234567 decimals permitted by Moi!

Radius found of the red Circle : 0,9281914 (max definition)
Here x = 1
Five points of the pentagon will be on the circle!

Of course when you have this first solution any resize will give you the other infinite solutions! :)

After the third C point i ask the length of the segment... if not 1 i draw another one C ! (up or down following results) :)





https://moiscript.weebly.com/uploads/3/9/3/8/3938813/longueur1.3dm

Ps seems there is something ultra simple that i have seen in writing this! :)

Intolerable suspense! :) I must verified my intuition!