Small challenge
06-07-2017, 03:49 PM (This post was last modified: 06-07-2017 04:11 PM by Pekis.)
Post: #5
 Pekis Member Posts: 120 Joined: Aug 2014
RE: Small challenge
(06-07-2017 11:35 AM)PedroLeiva Wrote:
(06-07-2017 09:53 AM)Pekis Wrote:  Hello,

...

Can you provide a numerial exaple to test?. TYVM, Pedro

Hello,

Here is a numerical example:
cex=0 (Outer Circle centered at (0,0))
cey=0
r=5 (Outer circle Radius)
c=0.2 (Fraction of Outer circle radius left for the triangle)
a=(sqrt(3)*(c-1)+sqrt((c+1)*(3-c)))/2=0.223694816
d=a*r=1.11847408 (Side length of equilateral triangle)
t=40° (0.6981317008 rad) (Angle at B)
Ax=cex+r*(1-c)*cos(t)=3.064177772
Ay=cey+r*(1-c)*sin(t)=2.571150439
Cx=Ax+d*sin(PI/3-t)=3.446718437
Cy=Ay+d*cos(PI/3-t)=3.622172279
Dx=Ax+d*cos(t-PI/6)=4.165659718
Dy=Ay+d*sin(t-PI/6))=2.765371425
Bx=cex+r*cos(t)=3.830222216
By=cey+r*sin(t)=3.213938048
Ex=cex+(r*(1-c)+d*cos(PI/6))*cos(t)=3.806189078
Ey=cey+(r*(1-c)+d*cos(PI/6))*sin(t)=3.193771851

Distance OA=sqrt((Ax-cex)^2+(Ay-cey)^2)=4
OK Distance OA=4=r*(1-c)
Distance AE=sqrt((Ax-Ex)^2+(Ay-Ey)^2)=0.9686269669
Distance EB=sqrt((Ex-Bx)^2+(Ey-By)^2)=0.03137303338
OK Distance AB=Distance AE+Distance EB=1=r*c
Distance AC=sqrt((Ax-Cx)^2+(Ay-Cy)^2)=1.11847408
Distance CD=sqrt((Cx-Dx)^2+(Cy-Dy)^2)=1.11847408
Distance DA=sqrt((Dx-Ax)^2+(Dy-Ay)^2)=1.11847408
OK Distance AC=Distance CD=Distance DA=d => Equilateral

CQFD
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 Messages In This Thread Small challenge - Pekis - 06-06-2017, 08:05 AM RE: Small challenge - pier4r - 06-06-2017, 01:26 PM RE: Small challenge - Pekis - 06-07-2017, 09:53 AM RE: Small challenge - PedroLeiva - 06-07-2017, 11:35 AM RE: Small challenge - Pekis - 06-07-2017 03:49 PM RE: Small challenge - PedroLeiva - 06-08-2017, 12:59 PM RE: Small challenge - Jim Horn - 06-07-2017, 04:25 PM RE: Small challenge - Pekis - 06-07-2017, 04:31 PM RE: Small challenge - SlideRule - 06-07-2017, 08:42 PM RE: Small challenge - Pekis - 06-07-2017, 09:54 PM RE: Small challenge - SlideRule - 06-07-2017, 10:53 PM RE: Small challenge - Pekis - 06-08-2017, 05:10 AM RE: Small challenge - SlideRule - 06-08-2017, 12:12 PM RE: Small challenge - Vtile - 06-09-2017, 01:14 PM RE: Small challenge - Csaba Tizedes - 06-11-2017, 10:59 AM RE: Small challenge - Pekis - 06-09-2017, 07:08 AM RE: Small challenge - Pekis - 06-11-2017, 09:58 PM

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