For any given triangle and x value if I keep translating the two purple vectors down along the median, will they eventually both intersect A and B at the same time?
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$\begingroup$ Let third vertex is C and middle of AB is D. Let move origin of purple vectors in direction DC. Then let find position of origin C$_1$ when left purple vector will point to A direction (but end of this vector is not A in this moment) and let find position of origin C$_2$ when right purple vector will point to B direction. Question is if C$_1$ and C$_2$ is the same point. Is it correct? $\endgroup$– Ivan KaznacheyeuSep 13, 2022 at 15:29
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$\begingroup$ In order to show this fact, one can consider similar triangles DE$_1$C and DAC$_1$, where E$_1$ are initial position of end of left purple vector. And the same for right purple vector. $\endgroup$– Ivan KaznacheyeuSep 13, 2022 at 15:33
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