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Omni-MATH / (*) Let ABC be a triangle with ∠ABC obtuse. The A -excircle is a circle in the exterior of △ABC that is tangent to side (BC)¯ of the triangle and tangent to the extensions of the o…

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problem

$(*)$ Let ABCABC be a triangle with ∠ABC\angle ABC obtuse. The AA -excircle is a circle in the exterior of △ABC\triangle ABC that is tangent to side BC¯\overline{BC} of the triangle and tangent to the extensions of the other two sides. Let EE , FF be the feet of the altitudes from BB and CC to lines ACAC and ABAB , respectively. Can line EFEF be tangent to the AA -excircle?
Plain-text mathematical notation (without MathML)
$(*)$ Let ABC be a triangle with ∠ABC obtuse. The A -excircle is a circle in the exterior of △ABC that is tangent to side (BC)¯ of the triangle and tangent to the extensions of the other two sides. Let E , F be the feet of the altitudes from B and C to lines AC and AB , respectively. Can line EF be tangent to the A -excircle?
Original LaTeX notation
$(*)$ Let $ABC$ be a triangle with $\angle ABC$ obtuse. The $A$ -excircle is a circle in the exterior of $\triangle ABC$ that is tangent to side $\overline{BC}$ of the triangle and tangent to the extensions of the other two sides. Let $E$ , $F$ be the feet of the altitudes from $B$ and $C$ to lines $AC$ and $AB$ , respectively. Can line $EF$ be tangent to the $A$ -excircle?

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Source and history

task_id
990b7f4e-9dde-57b4-8e8e-4dfceac46043
task_key
test--990b7f4e-9dde-57b4-8e8e-4dfceac46043
task_revision_id
1
config / split
/ test

Official source

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