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Infographic Geometry Problem 1062: Scalene Triangle with an angle of 60 degrees, Euler Line, Orthocenter, Circumcenter, Distance, Congruence, Transversal. Level: High School, SAT Prep, College, Mathematics Education

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The figure shows a scalene triangle ABC with the circumcircle of center O and angle B = 60 degrees. The Euler line OH intersects arc AB, AB, BC, and arc BC at C2, C1, A1, and A2, respectively. Prove that (1) OH = C1C2 - A1A2; (2) OH = AC1 - CA1; (3) OH = AB - BC; (4) OC1 = HA1.
 

Infographic Geometry problem: Scalene Triangle with an angle of 60 degrees, Euler Line, Orthocenter, Circumcenter, Distance, Congruence
 

 



 

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1061-1070 | Triangle | Circumcircle | Circle | 60 degrees | Euler Line | Orthocenter | Transversal Lines | Email | Solution / comment | by Antonio Gutierrez
Last updated: Nov 20, 2014