I have two circles and tangential line segments that I want to define a region:
center1={0,0};
center2={8,0};
radius1 = 4;
radius2 = 3;
circle1=Circle[center1,radius1];
circle2=Circle[center2,radius2];
endpoint1={x1,y1};
endpoint2={x2,y2};
tangent={endpoint1,endpoint2}/.Solve[{
(endpoint2-center2).(endpoint2-endpoint1)==0,
(endpoint1-center1).(endpoint2-endpoint1)==0,
(endpoint1-center1).(endpoint1-center1)==radius1^2,
(endpoint2-center2).(endpoint2-center2)==radius2^2,
(endpoint1-center1).(endpoint2-center2)>0},
{x1,y1,x2,y2},Reals]
Graphics[{circle1,circle2, Line[tangent]}]
How can I delete the inner arcs of the circles and create a region that is bounded by the outer lines and arcs of the shape?
I have Mathematica 10.1 so I can use the latest functions in Geometry.