Let ABC be a triangle and let a line / intersect the AB, BC, AC at C,A,B respectively. Let P be the corresponding Miquel point. Prove that the orthogonal projections of P on the lines AB, AC, BC and l are collinear.

Let ABC be a triangle and let a line / intersect the AB, BC, AC at C,A,B respectively. Let P be the corresponding Miquel point. Prove that the orthogonal projections of P on the lines AB, AC, BC and l are collinear.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.1: Early Definitions And Postulates

Problem 37E: Line l is parallel to plane P that is, it will not intersect P even if extended. Line m intersects...

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Question

Let ABC be a triangle and let a line / intersect the AB, BC, AC at C,A,B respectively. Let P
be the corresponding Miquel point. Prove that the orthogonal projections of P on the lines AB,
AC, BC and l are collinear.

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