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.