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OlympiadBench / 2099 / Let ABC be a triangle with AB=AC. The angle bisectors of A and B…

Problem

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

answer type

Numerical

is multiple answer

true

language

English

question

Let

A B C

be a triangle with

A B=A C

. The angle bisectors of

A

and

B

meet the sides

B C

and

A C

D

and

E

, respectively. Let

K

be the incenter of triangle

A D C

. Suppose that

\angle B E K=45^{\circ}

. Find all possible values of

\angle B A C

Plain-text mathematical notation (without MathML)

Let ABC be a triangle with AB=AC. The angle bisectors of A and B meet the sides BC and AC in D and E, respectively. Let K be the incenter of triangle ADC. Suppose that ∠BEK=45^(∘). Find all possible values of ∠BAC.

Original LaTeX notation

Let $A B C$ be a triangle with $A B=A C$. The angle bisectors of $A$ and $B$ meet the sides $B C$ and $A C$ in $D$ and $E$, respectively. Let $K$ be the incenter of triangle $A D C$. Suppose that $\angle B E K=45^{\circ}$. Find all possible values of $\angle B A C$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2099
task_id: 35b972d5-76f0-5722-aa30-b21ccb554093
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2099
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import