The problem says that if $A,B,C$ are three collinear points and $D,E,F$ also are three collinear points, and the intersections of the lines $\overline{AB},\overline{AF},\overline{BF}$ with the lines $\overline{DB},\overline{DC},\overline{EC}$ are the points $P,Q,R$ respectively, then this three points are also collinear. We have to prove this using the triangle $\bigtriangleup{XYZ}$ (but it doesn't make sense to me, please help).
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P.D. Sorry I didn't noticed that you have to click the attachment to see the image – opaloqwerty Dec 01 '19 at 03:21
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What theorems did not learnt about triangles? – Arctic Char Dec 01 '19 at 03:40
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1Menelaus is your friend. https://en.m.wikipedia.org/wiki/Menelaus%27s_theorem – WhatsUp Dec 01 '19 at 03:59
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Your AB has to AE? – Moti Dec 01 '19 at 06:15
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You can use projection to show that this may be proved for parallel lines. – Moti Dec 01 '19 at 06:16
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it could be useful this related question about proving pascal theorem which is a generalization – Dabed Dec 03 '19 at 05:03