Brain Teaser 2 - Unusual challenge

[fhub]

(01-18-2016 02:17 PM)Pekis Wrote:  What are the coordinates of the point (xp,yp) on the image, equidistant (shortest) from the 3 figures ? Which distance ?

How did you get this ? Please provide maximum precision. Good luck !

Here are my results:

Code:


;distance to line:     dl=abs(x0-y0-2)/sqrt(2)
;distance to circle:   dc=sqrt(x0^2+y0^2)-sqrt(2)
;distance to parabola: dp=sqrt((x0-xs)^2+(y0-xs^2-1)^2)
;condition for xs (x-coord of intersection point with parabola):
;2*xs^3-(2*y0-3)*xs-x0=0

;equation system: dl=dc && dl=dp && equation for xs
abs(x0-y0-2)/sqrt(2)=sqrt(x0^2+y0^2)-sqrt(2)
abs(x0-y0-2)/sqrt(2)=sqrt((x0-xs)^2+(y0-xs^2-1)^2)
2*xs^3-(2*y0-3)*xs-x0=0
;distance
dl=abs(x0-y0-2)/sqrt(2)

Solution:
---------
Variables:
  x0       = +1.9852721593222333   
  y0       = +1.529294579719819   
  xs       = +1.007327946198892   
  dl       = +1.0917887237671993

Franz