

Geometry Problem 1122:
Triangle, 90 Degree, Perpendicular Lines, Orthocenter,
Altitude, Midpoint, Collinear Points. Level: High School, SAT Prep,
Honors Geometry, College, Math Education
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The figure below shows a triangle ABC
with orthocenter H. Lines L_{1} and L_{2} are perpendicular
at B.
AH extended meets L_{1} and L_{2} at A_{1} and A_{2}, respectively. CH
extended meets L_{1} and L_{2} at C_{1} and C_{2}, respectively. AC extended
meets L_{1} and L_{2} at B_{1} and B_{2}. Prove that midpoints of A_{1}A_{2},
B_{1}B_{2}, and C_{1}C_{2} are collinear.

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