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 Midpoint:  The point on a line segment that divides it into two equal parts.

Equidistant Chords: Determine the relationship between two segments that have endpoints on a circle, if the segments are the same perpendicular distance away from the center of the circle.

Medial Polygons: Investigate the characteristics of a polygon that is generated by connecting the midpoints of consecutive sides of a polygon.

Quadrilaterals Inscribed in Quadrilaterals: Explore properties of quadrilaterals constructed using the midpoint of given quadrilaterals.

Finding the Midpoint: How do the coordinates of a midpoint of a segment relate to the coordinates of the endpoints?

Maximum quadrilateral: Given three fixed line segments, find a fourth line segment such that the resulting quadrilateral formed by the four segments has maximum area.