Online Geometry Problems

Online Geometry Problem 929: Triangle, Orthocenter, Circumcircle, Reflection, Concurrency. Level: High School, SAT Prep, College, Mathematics Education

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The figure below shows a triangle ABC. A line that passes through the orthocenter H intersects AB, BC, and CA extended at D, E, and F, respectively. A1 is the reflection of D on BC, B1 is the reflection of E on AC, and C1 is the reflection of E on AB. Prove that (1) A1E, B1F, and C1D are concurrent at P. (2) P is on the circumcircle O.


 

Geometry Problem 929: Triangle, Orthocenter, Circumcircle, Reflection, Concurrency


 

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