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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 O1, O2, and O). O3 and O4 are the midpoints of arcs AB and BC, respectively. Circle of center O3 and radius O3B cuts arcs BC and AC at D and E, respectively. Circle of center O4 and radius O4B 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.
 
 

Construction of the Inscribed Circle of the Arbelos, Semicircles, Diameter, Circle, Triangle, Circumcircle, Tangent
 

 



 

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1161-1170 | Arbelos | Semicircle | Circle | Tangent Circles | Midpoint | Circumcircle | Email | Post a Solution / comment | by Antonio Gutierrez
Last updated: Nov 30, 2015