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Geometry Problem 730: Triangle, Altitude, Orthocenter, Perpendicular, Concurrent Lines. Level: High School, Honors Geometry, College, Mathematics Education

The diagram shows a triangle ABC with the altitudes AA1, BB1, and CC1. A1A2, is perpendicular to AB, A1A3, is perpendicular to AC and AA4 is perpendicular to A2A3. Similarly BB4 is perpendicular to B2B3, and CC4 is perpendicular to C2C3. Prove that AA4, BB4 , and CC4 are concurrent.

Triangle, Altitude, Orthocenter, Concurrent lines


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