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locus of concurrency point as a line turns about a point

Source: IMAR 2011 p1

September 26, 2018
geometryLocusconcurrencyconcurrentLocus problems

Problem Statement

Let A0A1A2A_0A_1A_2 be a triangle and let PP be a point in the plane, not situated on the circle A0A1A2A_0A_1A_2. The line PAkPA_k meets again the circle A0A1A2A_0A_1A_2 at point Bk,k=0,1,2B_k, k = 0, 1, 2. A line ℓ\ell through the point PP meets the line Ak+1Ak+2A_{k+1}A_{k+2} at point Ck,k=0,1,2C_k, k = 0, 1, 2. Show that the lines BkCk,k=0,1,2B_kC_k, k = 0, 1, 2, are concurrent and determine the locus of their concurrency point as the line ℓ\ell turns about the point PP.
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