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Omni-MATH / In △ABC, the external angle bisector of ∠BAC intersects line BC at D. E is a point on ray (AC)→ such that ∠BDE=2∠ADB. If AB=10,AC=12, and CE=33, compute (DB)/(DE).

Problem

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problem

In △ABC\triangle ABC, the external angle bisector of ∠BAC\angle BAC intersects line BCBC at DD. EE is a point on ray AC→\overrightarrow{AC} such that ∠BDE=2∠ADB\angle BDE=2 \angle ADB. If AB=10,AC=12AB=10, AC=12, and CE=33CE=33, compute DBDE\frac{DB}{DE}.
Plain-text mathematical notation (without MathML)
In △ABC, the external angle bisector of ∠BAC intersects line BC at D. E is a point on ray (AC)→ such that ∠BDE=2∠ADB. If AB=10,AC=12, and CE=33, compute (DB)/(DE).
Original LaTeX notation
In \(\triangle ABC\), the external angle bisector of \(\angle BAC\) intersects line \(BC\) at \(D\). \(E\) is a point on ray \(\overrightarrow{AC}\) such that \(\angle BDE=2 \angle ADB\). If \(AB=10, AC=12\), and \(CE=33\), compute \(\frac{DB}{DE}\).

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Source and history

task_id
984d3112-db47-57a4-aaf2-eed44282bc2b
task_key
test--984d3112-db47-57a4-aaf2-eed44282bc2b
task_revision_id
1
config / split
/ test

Official source

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