|Re: Help with geometry problem required|
Message #39 Posted by C.Ret on 22 Jan 2013, 8:47 a.m.,
in response to message #32 by Harald
My best investigation and computation of radius r and vector length x give me the following figure.
As can be seen, the three vectors length is about x= 0.4226 (based on unit great circle R = 1 ) and the inner circle is limited by orthogonal axis of the quadrant r = 0.4082 (when great circle is R = 1).
This show that actually to contact points are present respectively Ix and Iy.
The (OA) segment is one radius of the great (red) circle; OA = R leading to eq.1
As explain in this threat, due to symmetry, the angle between O'C vector (respectively O'B) and vertical axe O'Ix (respectively horizontal axe O'Bx) is 15 leading to eq.2
Solving this system as a function of R is trivial:
Value of r is deduce from (eq. 2).
One may also use this code to get numerical result on his ageless HP classic:
01 LBL A
05 sqrt x
06 GSB 9
09 LBL 9
Enter radius R of great circle.Execute code. Radius of inner circle is displayed, lenght of vector is store in stack register y:
5 [ A ] 2.0412 [ x<>y ] 2.1132
Edited: 22 Jan 2013, 11:50 a.m. after one or more responses were posted