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Let P be any point inside triangle ABC as shown. Draw the lines PA, PB, and PC. These lines meet the circle inscribed in the triangle at points X, Y, and Z, respectively. The inscribed circle touches the sides of the triangle at points D, E, and F, as shown. Then, no matter where point P is chosen, the lines DX, EY, and FZ will always meet at a point (labelled Q in the figure).
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