Eventually I found the solution. The belt problem helped me a lot.
Belt problem - Wikipedia, the free encyclopedia
Please refer to the figure for the solution.
I am sure this is a basic problem but I am not able to find a solution to it. I have two inner tangents to two circles as shown in the figure (The figure is just for reference and not drawn with exact measurements). The horizontal distance between the centers of the two circles is 45 and vertical distance is 150. The units are irrelevant. The radii of the two circles are 40 and 50 respectively.
I would like to estimate the angles 'a' and 'b' that the tangents make with the vertical. I checked the following link but did not follow their solution.
Circle-Circle Tangents -- from Wolfram MathWorld
If someone can solve it with one example then it would be a great help.