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Omni-MATH / Let ABC be a triangle with AB=13,AC=14, and BC=15. Let G be the point on AC such that the reflection of BG over the angle bisector of ∠B passes through the midpoint of AC. Let Y be…

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problem

Let ABCA B C be a triangle with AB=13,AC=14A B=13, A C=14, and BC=15B C=15. Let GG be the point on ACA C such that the reflection of BGB G over the angle bisector of ∠B\angle B passes through the midpoint of ACA C. Let YY be the midpoint of GCG C and XX be a point on segment AGA G such that AXXG=3\frac{A X}{X G}=3. Construct FF and HH on ABA B and BCB C, respectively, such that FX‖BG‖HYF X\|B G\| H Y. If AHA H and CFC F concur at ZZ and WW is on ACA C such that WZ‖BGW Z \| B G, find WZW Z.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=13,AC=14, and BC=15. Let G be the point on AC such that the reflection of BG over the angle bisector of ∠B passes through the midpoint of AC. Let Y be the midpoint of GC and X be a point on segment AG such that (AX)/(XG)=3. Construct F and H on AB and BC, respectively, such that FX‖BG‖HY. If AH and CF concur at Z and W is on AC such that WZ‖BG, find WZ.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=13, A C=14$, and $B C=15$. Let $G$ be the point on $A C$ such that the reflection of $B G$ over the angle bisector of $\angle B$ passes through the midpoint of $A C$. Let $Y$ be the midpoint of $G C$ and $X$ be a point on segment $A G$ such that $\frac{A X}{X G}=3$. Construct $F$ and $H$ on $A B$ and $B C$, respectively, such that $F X\|B G\| H Y$. If $A H$ and $C F$ concur at $Z$ and $W$ is on $A C$ such that $W Z \| B G$, find $W Z$.

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task_id
2f2c64af-2a15-5fb1-9eb6-5abd146a159c
task_key
test--2f2c64af-2a15-5fb1-9eb6-5abd146a159c
task_revision_id
1
config / split
/ test

Official source

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