2003 Pan African MO Problems/Problem 2
The circumference of a circle is arbitrarily divided into four arcs. The midpoints of the arcs are connected by segments. Show that two of these segments are perpendicular.
Let in that order be the four points that divide the circle into four arcs. Let be the midpoints of respectively, and let be the intersection of and . Additionally, let and .
Note that . Additionally, from the definition of midpoint, and . Thus, . Likewise, and , so . Therefore, , so .
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