GoGeometry Action 148!

Creation of this resource was inspired by a tweet from Antonio Gutierrez (GoGeometry). Both circles you see are externally tangent to each other. In addition, both lines you see are externally tangent to both circles. Note: The LARGE POINTS are MOVEABLE.
Now, here's another question: We now know that the areas of both manila triangles (shown below) are equal. Yet how can we prove that the area of the green quadrilateral = double the area of one of these triangles?

Slide the slider for a hint! (What can we conclude about the gray triangles? How does this help us?)

Quick (Silent) Demo