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Geometry Problem 1137: Triangle, Circumcircle, Orthocenter, Midpoint, Arc, Collinear Points, Tangent Circles. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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In a triangle ABC (figure below) with circumcircle O, altitude BD, and orthocenter H, M is the midpoint of AC. MH extended cuts the arc BC at E. Circle of center O1 and diameter HE cuts circle O at F. If O2 is the circumcenter of triangle FDM, prove that (1) Points F, O1, and O2 are collinear; (2) Circles O2 and O1 are tangent at F.


 

Infographic Geometry problem 1137 Triangle, Circumcircle, Orthocenter, Midpoint, Arc, Collinear Points, Tangent Circles
 

 

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Last updated: Jul 15, 2015 by Antonio Gutierrez.