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Omni-MATH / Let ABC be a triangle with ∠BAC=60^(∘). Let AP bisect ∠BAC and let BQ bisect ∠ABC, with P on BC and Q on AC. If AB+BP=AQ+QB, what are the angles of the triangle?

Problem

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problem

Let ABCABC be a triangle with ∠BAC=60∘\angle BAC = 60^{\circ}. Let APAP bisect ∠BAC\angle BAC and let BQBQ bisect ∠ABC\angle ABC, with PP on BCBC and QQ on ACAC. If AB+BP=AQ+QBAB + BP = AQ + QB, what are the angles of the triangle?
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with ∠BAC=60^(∘). Let AP bisect ∠BAC and let BQ bisect  ∠ABC, with P on BC and Q on AC. If AB+BP=AQ+QB, what are the angles of the triangle?
Original LaTeX notation
Let $ABC$ be a triangle with $\angle BAC = 60^{\circ}$. Let $AP$ bisect $\angle BAC$ and let $BQ$ bisect  $\angle ABC$, with $P$ on $BC$ and $Q$ on $AC$. If $AB + BP = AQ + QB$, what are the angles of the triangle?

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Source and history

task_id
501367d5-d538-5c8f-a912-e25062026792
task_key
test--501367d5-d538-5c8f-a912-e25062026792
task_revision_id
1
config / split
/ test

Official source

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