How to join overlapping circles?

Question

I want to visually join two circles that are overlapping so that

becomes

Answer 1

Don't have the time to solve it right now. But I'll give you what you need to work it out:

http://en.wikipedia.org/wiki/Triangle#The_sine.2C_cosine_and_tangent_rules

In the picture on wikipedia you see the triangle A,B,C. Let A be the center of the left circle, B the center of the right circle. And AC the radius of the left circle and BC the radius of the right circle.

Then point C would be the top intersection point. The corner in A, α, is half the angle in the left circle.The corner in b, β, half the angle in the right circle. These are the angles you need, right?

Wikipedia explains further: 'If the lengths of all three sides of any triangle are known the three angles can be calculated.'

Pseudocode:

a=radius_a
b=radius_b
c=b_x - a_x
alpha=arccos((b^2 + c^2 - a^2) / (2*b*c)) //from wikipedia
left_angle=2*alpha

Good luck :)