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
Hi,
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 I_{x} and I_{y}.
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'I_{x} (respectively horizontal axe O'B_{x}) is 15‹ leading to eq.2
Solving this system as a function of R is trivial:
(eq.3)
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
02 1
03 DEG
04 2
05 sqrt x
06 GSB 9
07 +
08 ÷
08 ENTER^
09 LBL 9
10 1
11 5
12 COS
13 *
14 RTN
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
