Show that line BAC is longest when lines BD and CD pass through the centers of the circles. Also show that line BAC is perpendicular to line AD when this happens.
- Notice that angles B and C don't change as line BAC is rotated about point A. (Investigate some of the posts below with the large yellow circles.)
- This means that all triangles BDC are similar (have the same shape, but differ in size). So all sides of triangle BDC must maximize at the same time.
- Note also that the line between the centers of the circles is perpendicular to line AD, because the two circles are symmetric about the horizontal line drawn through their centers.
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