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Simson lines of opposite points are perpendicular

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April 19, 2013
geometrycircumcircle

Problem Statement

It is known that for any point PP on the circumcircle of a triangle ABCABC, the orthogonal projections of PP onto AB,BC,CAAB,BC,CA lie on a line, called a Simson line of PP. Show that the Simson lines of two diametrically opposite points P1P_1 and P2P_2 are perpendicular.
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