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Omni-MATH / In triangle ABC, let J be the center of the excircle tangent to side BC at A₁ and to the extensions of the sides AC and AB at B₁ and C₁ respectively. Suppose that the lines A₁B₁ an…

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problem

In triangle ABCABC, let JJ be the center of the excircle tangent to side BCBC at A1A_{1} and to the extensions of the sides ACAC and ABAB at B1B_{1} and C1C_{1} respectively. Suppose that the lines A1B1A_{1}B_{1} and ABAB are perpendicular and intersect at DD. Let EE be the foot of the perpendicular from C1C_{1} to line DJDJ. Determine the angles ∠BEA1\angle{BEA_{1}} and ∠AEB1\angle{AEB_{1}}. [i]
Plain-text mathematical notation (without MathML)
In triangle ABC, let J be the center of the excircle tangent to side BC at A₁ and to the extensions of the 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.

[i]
Original LaTeX notation
In triangle $ABC$, let $J$ be the center of the excircle tangent to side $BC$ at $A_{1}$ and to the extensions of the sides $AC$ and $AB$ at $B_{1}$ and $C_{1}$ respectively. Suppose that the lines $A_{1}B_{1}$ and $AB$ are perpendicular and intersect at $D$. Let $E$ be the foot of the perpendicular from $C_{1}$ to line $DJ$. Determine the angles $\angle{BEA_{1}}$ and $\angle{AEB_{1}}$.

[i]

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Source and history

task_id
6941776c-f97a-5296-ad1d-4691d903e6e6
task_key
test--6941776c-f97a-5296-ad1d-4691d903e6e6
task_revision_id
1
config / split
/ test

Official source

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