Little explorations with HP calculators (no Prime)

[pier4r]

(03-28-2017 05:33 PM)Dieter Wrote:  What? No clue? Really ?-)

Take a look at the picture. From the upper left corner to the point where the circle touches the arc it's √2 · d/2 plus d/2, and this sum is 10. This directly leads to d = 20/(1+√2) or 8,284. Expand this with 1–√2 to get d = 20 · (√2–1). So a=20, b=2, c=1, and the desired value is floor(1600/23) = 69.

Dieter

Thanks for the contribution, my only clue (see image below) died immediately because I did try to determine the x in the image but I failed with my rusty knowledge. And if your solution is correct (we need peer review here) then my program fails even to capture the solution.

http://i.imgur.com/24nmK1G.jpg

Could you explain (or hint a known relationship) how did you get that d/2+x = d/2*sqrt(2) ?