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Omni-MATH / Let ABC be a triangle with AB=5,AC=4,BC=6. The angle bisector of C intersects side AB at X. Points M and N are drawn on sides BC and AC, respectively, such that (XM)¯‖(AC)¯ and …

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problem

Let ABCA B C be a triangle with AB=5,AC=4,BC=6A B=5, A C=4, B C=6. The angle bisector of CC intersects side ABA B at XX. Points MM and NN are drawn on sides BCB C and ACA C, respectively, such that XM¯‖AC¯\overline{X M} \| \overline{A C} and XN¯‖BC¯\overline{X N} \| \overline{B C}. Compute the length MNM N.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=5,AC=4,BC=6. The angle bisector of C intersects side AB at X. Points M and N are drawn on sides BC and AC, respectively, such that (XM)¯‖(AC)¯ and (XN)¯‖(BC)¯. Compute the length MN.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=5, A C=4, B C=6$. The angle bisector of $C$ intersects side $A B$ at $X$. Points $M$ and $N$ are drawn on sides $B C$ and $A C$, respectively, such that $\overline{X M} \| \overline{A C}$ and $\overline{X N} \| \overline{B C}$. Compute the length $M N$.

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Source and history

task_id
e82c887d-c7f4-5bcc-a998-d9bc2fa88c8b
task_key
test--e82c887d-c7f4-5bcc-a998-d9bc2fa88c8b
task_revision_id
1
config / split
/ test

Official source

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