Linkage & Locus

Level pending

Quadrilateral A B C D ABCD is self-intersecting in a very specific way; the midpoints of A B \overline{AB} and C D \overline{CD} coincide. If B C = C D = D A BC=CD=DA , and we keep A B \overline{AB} fixed, then the locus of all possible locations of point C C is

an ellipse not a conic section a circle a parabola

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