

Geometry Problem 1168: Construction
of the Inscribed Circle of the Arbelos,
Semicircles, Diameter, Circle,
Triangle, Circumcircle, Tangent. Level: High School, College, Math Education,
Tutoring
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The figure shows an arbelos ABC (AB, BC, and AC are semicircles
of centers O_{1}, O_{2}, and O). O_{3}
and O_{4} are the midpoints of arcs AB and BC,
respectively. Circle of center O_{3} and radius O_{3}B cuts arcs BC
and AC at D and E, respectively. Circle of center O_{4}
and radius O_{4}B cuts arc AB at F. Prove that the
circumcircle of triangle DEF is the inscribed circle of the
arbelos ABC.. See also:
Isolines Artwork Problem
1168.







