Squares on a Line Segment
Squares on a Line Segment
A segment is given and on it the point . On the same side of , the squares and are constructed. The circumcircles of the two squares, whose centers are and , intersect at and another point .
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AB
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N
(a) Prove that lines and intersect at .
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BK
N
(b) Prove that all such constructed lines pass through the same point , regardless of the selection of .
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M
(c) Find the locus of the midpoints of all segments , as varies along the segment .
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AB