Proving X, A, and Y Lie in a Straight Line | Triangle Medians Proof

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To prove that points X, A, and Y lie in a straight line, the discussion emphasizes using indirect proof and constructing specific segments. By connecting points C and X, as well as B and Y, a clearer geometric figure emerges that aids in the proof. The importance of a precise drawing is highlighted to visualize the relationships between the points. The conversation suggests that careful analysis of the triangle's medians and their extensions will lead to the desired conclusion. A thorough understanding of triangle properties is essential for this proof.
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This is question I am really stuck with, please help if you can. (Its by indirect proof).
Question: The medians BD and CE in triangle ABC are produced to X and Y respectively so that BD = DX and CE = EY. Prove that X, A, and Y lie in a straight line.
 
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Here is what I have so far:
 

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No need in absurdum!

Connect C and X and see what helpful figure you are getting.
Same for B and Y.
Precise drawing would help.
 

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