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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 L1 and L2 are perpendicular
at B.
AH extended meets L1 and L2 at A1 and A2, respectively. CH
extended meets L1 and L2 at C1 and C2, respectively. AC extended
meets L1 and L2 at B1 and B2. Prove that midpoints of A1A2,
B1B2, and C1C2 are collinear.
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