SOLUTION: Centers of two circles with radiuses 3cm and 2cm are 20 cm apart. what is the angle between the line that connects the centers and line that is tangent line to both circles?

Make a sketch.


In the sketch, draw the radii of the circles to the tangent points.


Notice that the radii are parallel, since they BOTH are perpendicular to the tangent line.


From the center of the smaller circle, draw the line parallel to the tangent line.


You will get a right angled triangle with the hypotenuse length of 20 cm.


One of its leg is  3-2 = 1 cm long.


Hence,  sin(a) =  = 0.05, where "a" is the sought angle.


So, a = arcsin(0.05) = 0.050021 radians = 2.865 degrees   (rounded).      ANSWER