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Four Collinear Points Related to the Altitudes

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Let ABC be a triangle. Let A', B', and C' be the feet of the altitudes from A, B, and C. Let P and Q be the projections of A' to AB and AC. Let R and S be the projections of A' to BB' and CC'. Then P, Q, R, and S are collinear.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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See problem 5 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 99.

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