Suppose we have two circles sharing same center
O. Circle 1 is defined by
r1 and circle 2 is defined by
r2. Lets say we pick an arbitrary point
A that lies on circumference of circle 1. If we strech this line
OA, it will cross circle 2 at point
B. If we define another line at point A with a specific angle
phi (in respect to line
AB), this new line will cross circle 2 at point
E. Now, Line
OB and line
OE are defining angle
theta. How can we find value of
theta?
If the above doesn't make much sense, then looking at the below figure only: If {
r1,
r2,
phi} are all known values, how can we calculate
theta?
(http://img217.imageshack.us/img217/998/questionforvisguycomfor.jpg)
Thanks,
Yousuf.
Though my answer may include many mistakes.
I haven't followed thru all of JuneTheSecond's math, but, he's usually correct. However, most trig / geo reference books should contain formulas since you know two sides & an angle of a triangle. The sides would be OA & OE (the two radii), and the angle, OAE, which is 180 - phi.
HTH
Wapperdude
A quick check of Math Table & Formula Handbook provides the necessary equations, see attached pdf.
Found my mistake in the last lines.
Ok, the problem is solved using the following equation (following wapperdude advice):
(http://img16.imageshack.us/img16/998/questionforvisguycomfor.jpg)
theta = phi–ASIN(r1/r2*SIN(PI()–phi))
Note, I have verified this equation with numbers and it gave me correct results.
Thanks alot wapperdude
Yousuf.
JuneTheSecond,
I appreciate your efforts trying to help me.. but unfortunately i wasn't able to follow your method:
- In step (7), I think there is a mistake (see figure below)
- I don't understand what did you do exactly to go from step (17) to step (18)
(http://img208.imageshack.us/img208/998/questionforvisguycomfor.jpg)
theta = ASIN(COS(
phi)*(
r1/
r2*SIN(
phi)
+SQRT(1-(
r1/
r2)^2*SIN(
phi)^2)))
I have tested your last equation (both cases
+ and
-) with numbers but it did not give me correct results.
Anyway, i got the correct equation as i showed in my previous reply (following wapperdude method).
Again, i really appreaciate all the efforts and and time you spent on this.
Thanks,
Yousuf.