Determine these two angle (Isosceles triangle) Please see the following diagram:
 
This is an isosceles triangle.
Let the angles be as follow: green = G, red = R, blue = B, purple = P
G = pi - 2B 
Now my question is.. Based on the value of blue angle (B)- is it possible to determine the R and P angles given the radius and arc length. The angles are formed by the tangent of the circles at the intersection point 
Arc length is the "outside" arc length, for example, for the bottom right circle, it goes from point G to point H. Radius is simple-
All circles have the same radius, R1=R2=R3. As for the arc length, I believe the two bottom circles have the same L1=L2, but the upper circles's will be different.
I tried working it out, I obtained the value for the purple angle to be : 2pi - L/R; Can someone verify this as well? I am mostly interested in the red angle.
Thank you!
 A: This is a complete rewrite of my previous post.
Assume $\tan B=h$. Up to a similarity transformation, the corners of your triangle will have the coordinates
$$A=\begin{pmatrix}-1\\0\end{pmatrix}\qquad
B=\begin{pmatrix}1\\0\end{pmatrix}\qquad
D=\begin{pmatrix}0\\h\end{pmatrix}$$
Now assume a circle radius $r$ and you can compute the points of intersection as
$$G=\begin{pmatrix}
\frac{h^{2} + \sqrt{-h^{4} + 4 \, {\left(h^{2} + 1\right)} r^{2} - 2 \, h^{2} - 1} h + 1}{2 \, {\left(h^{2} + 1\right)}} \\[2ex]
\frac{h^{3} + \sqrt{h^{2} + 1} \sqrt{-h^{2} + 4 \, r^{2} - 1} + h}{2 \, {\left(h^{2} + 1\right)}}
\end{pmatrix}\qquad
H=\begin{pmatrix}0 \\ -\sqrt{r^{2} - 1}\end{pmatrix}$$
Now the arc around point $B$ is
$$\frac{L_2}{R_2}=2\pi-
\arccos\frac{(G-B)\cdot(H-B)}{\lVert G-B\rVert\cdot\lVert H-B\rVert}$$
Plugging in the above coordinates, you can obtain a relation between $r$ and $\frac{L_2}{R_2}$, but that fraction is highly non-linear. Therefore it is very difficult to compute $r$ given $\frac{L_2}{R_2}$. So it should be possible to solve this numerically for a given set of numbers, but I doubt I'll be able to come up with a general closed formula for the angles.
