MathDB
concurrence

Source: Taiwan 3rd TST 2005, 3rd independent study, problem 2

August 12, 2005
geometry proposedgeometry

Problem Statement

Given a triangle ABCABC, A1A_1 divides the length of the path CABCAB into two equal parts, and define B1B_1 and C1C_1 analogously. Let lAl_A, lBl_B, lCl_C be the lines passing through A1A_1, B1B_1 and C1C_1 and being parallel to the bisectors of ∠A\angle A, ∠B\angle B, and ∠C\angle C. Show that lAl_A, lBl_B, lCl_C are concurrent.
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