Hello, Encircled!
I want to determine the circle through points N, S and V.
I know the distance between N and S.
I know the angle NVS.
How could an expression describing such a circle be constrained given that information?We have a circle with centerCode:* * * * * * d/2 M d/2 * N o- - - - + - - - -o S \ * | * / * \ * θ|θ *r / * * \ o / * * \ O / * \ / * \ / * * \ / * * \θ/ * * o * V
Chord
. . Midpoint
Angle
Draw radii
In
Therefore: .
I rephrased the question here:
Want radius of circle through 3 points. A chord and an angle are known.
(Because at first I actually failed to find this, my own, old thread, duh)
Please see it in order to maybe clearer understand what I'm looking for.
And actually, now when I look at it, there are some misunderstandings in this thread here.
earboth:
I do not know angles x or y. I only know the angle NVS = x+y.
So I can't solve for radius according to your formula there.
Soroban:
Why would angles NOS = 2 NVS, and MOS = NVS?
It looks wrong.
I borrow this fine ASCII art and introduce in it the point L.
Now, since L is on the opposite side of the chord, as seen from the circle origo O, does it still hold that the angle NLS = half the angle NOS?
It is supposed to hold for any point V on the same circle which the chord crosses, but intuitively, that angle seems much larger when V is at L on the smaller side of a chord. Is another relationship at play there?
Code:*L * * * * d/2 M d/2 * N o- - - - + - - - -o S \ * | * / * \ * θ|θ *r / * * \ o / * * \ O / * \ / * \ / * * \ / * * \θ/ * * o * V