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Omni-MATH / Consider triangle ABC with ∠A=2∠B. The angle bisectors from A and C intersect at D, and the angle bisector from C intersects (AB)¯ at E. If (DE)/(DC)=(1)/(3), compute (AB)/(AC).

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problem

Consider triangle ABCA B C with ∠A=2∠B\angle A=2 \angle B. The angle bisectors from AA and CC intersect at DD, and the angle bisector from CC intersects AB¯\overline{A B} at EE. If DEDC=13\frac{D E}{D C}=\frac{1}{3}, compute ABAC\frac{A B}{A C}.
Plain-text mathematical notation (without MathML)
Consider triangle ABC with ∠A=2∠B. The angle bisectors from A and C intersect at D, and the angle bisector from C intersects (AB)¯ at E. If (DE)/(DC)=(1)/(3), compute (AB)/(AC).
Original LaTeX notation
Consider triangle $A B C$ with $\angle A=2 \angle B$. The angle bisectors from $A$ and $C$ intersect at $D$, and the angle bisector from $C$ intersects $\overline{A B}$ at $E$. If $\frac{D E}{D C}=\frac{1}{3}$, compute $\frac{A B}{A C}$.

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Source and history

task_id
d84f3a1e-7816-56b2-98bb-9f079a1705b1
task_key
test--d84f3a1e-7816-56b2-98bb-9f079a1705b1
task_revision_id
1
config / split
/ test

Official source

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