Floor van Lamoen, Jigsawing a quadrangle from a triangle,
Forum Geometricorum, 13 (2013) 149--152.
Abstract. For an acute-angled triangle ABC, we construct two isotomic points P and Q on BC and P' and Q' on AB and AC respectively, such that BPP' and CQQ' are right triangles which, when rotated about P' and Q' respectively through appropriate angles fit with AP'Q' to a quadrangle with a new fourth vertex A'. We show that AA' passes trough the circumcenter O.
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