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OlympiadBench / 1760 / In triangle ABC, let J be the centre of the excircle tangent to side BC…

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

In triangle

A B C

, let

J

be the centre of the excircle tangent to side

B C

A_{1}

and to the extensions of sides

A C

and

A B

B_{1}

and

C_{1}

, respectively. Suppose that the lines

A_{1} B_{1}

and

A B

are perpendicular and intersect at

D

. Let

E

be the foot of the perpendicular from

C_{1}

to line

D J

. Determine the angles

\angle B E A_{1}

and

\angle A E B_{1}

Plain-text mathematical notation (without MathML)

In triangle ABC, let J be the centre of the excircle tangent to side BC at A₁ and to the extensions of sides AC and AB at B₁ and C₁, respectively. Suppose that the lines A₁B₁ and AB are perpendicular and intersect at D. Let E be the foot of the perpendicular from C₁ to line DJ. Determine the angles ∠BEA₁ and ∠AEB₁.

Original LaTeX notation

In triangle $A B C$, let $J$ be the centre of the excircle tangent to side $B C$ at $A_{1}$ and to the extensions of sides $A C$ and $A B$ at $B_{1}$ and $C_{1}$, respectively. Suppose that the lines $A_{1} B_{1}$ and $A B$ are perpendicular and intersect at $D$. Let $E$ be the foot of the perpendicular from $C_{1}$ to line $D J$. Determine the angles $\angle B E A_{1}$ and $\angle A E B_{1}$.

question type

Open-ended

subject

Math

unit

^{\circ}

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Source and history

upstream_id / Original problem ID: 1760
task_id: 7249cec5-74b8-5e48-93e1-64262939fd22
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1760
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import