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Concurrency with tangents to nine point circle

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December 31, 2011
geometry unsolvedgeometry

Problem Statement

Let ABCABC be a scalene triangle. Let lAl_A be the tangent to the nine-point circle at the foot of the perpendicular from AA to BCBC, and let lA′l_A' be the tangent to the nine-point circle from the mid-point of BCBC. The lines lAl_A and lA′l_A' intersect at A′A' . Define B′B' and C′C' similarly. Show that the lines AA′,BB′AA' , BB' and CC′CC' are concurrent.
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