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MATH / In triangle ABC, ∠ABC=90^(∘), and point D lies on segment (BC)¯ such that (AD)¯ is an angle bisector. If AB=12 and BD=4, then find AC.

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In triangle ABCABC, ∠ABC=90∘\angle ABC = 90^\circ, and point DD lies on segment BC¯\overline{BC} such that AD¯\overline{AD} is an angle bisector. If AB=12AB = 12 and BD=4BD = 4, then find ACAC.
Plain-text mathematical notation (without MathML)
In triangle ABC, ∠ABC=90^(∘), and point D lies on segment (BC)¯ such that (AD)¯ is an angle bisector.  If AB=12 and BD=4, then find AC.
Original LaTeX notation
In triangle $ABC$, $\angle ABC = 90^\circ$, and point $D$ lies on segment $\overline{BC}$ such that $\overline{AD}$ is an angle bisector.  If $AB = 12$ and $BD = 4$, then find $AC$.

level

Level 5

type

Geometry

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Source and history

task_id
9bcfd2d4-c651-5816-ab08-53d970a16644
task_key
geometry--test--9bcfd2d4-c651-5816-ab08-53d970a16644
task_revision_id
1
config / split
geometry / test

Official source

initial import