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St. Petersburg MO 2017 Grade 11 P5

Source: St. Petersburg MO 2017 Grade 11 P5

May 3, 2018
geometry

Problem Statement

Given a tetrahedron PABCPABC, draw the height PHPH from vertex PP to ABCABC. From point HH, draw perpendiculars HA’,HB’,HC’HA’,HB’,HC’ to the lines PA,PB,PCPA,PB,PC. Suppose the planes ABCABC and A’B’C’A’B’C’ intersects at line ℓ\ell. Let OO be the circumcenter of triangle ABCABC. Prove that OH⊥ℓOH\perp \ell.
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