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Omni-MATH / Let ABC be a triangle with ∠A=90^(∘) . Points D and E lie on sides AC and AB , respectively, such that ∠ABD=∠DBC and ∠ACE=∠ECB . Segments BD and CE meet at I . Determine whether or…

Problem

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problem

Let ABCABC be a triangle with ∠A=90∘\angle A = 90^{\circ} . Points DD and EE lie on sides ACAC and ABAB , respectively, such that ∠ABD=∠DBC\angle ABD = \angle DBC and ∠ACE=∠ECB\angle ACE = \angle ECB . Segments BDBD and CECE meet at II . Determine whether or not it is possible for segments AB,AC,BI,ID,CI,IEAB, AC, BI, ID, CI, IE to all have integer lengths.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with ∠A=90^(∘) . Points D and E lie on sides AC and AB , respectively, such that ∠ABD=∠DBC and ∠ACE=∠ECB . Segments BD and CE meet at I .  Determine whether or not it is possible for
segments AB,AC,BI,ID,CI,IE to all have integer lengths.
Original LaTeX notation
Let $ABC$ be a triangle with $\angle A = 90^{\circ}$ . Points $D$ and $E$ lie on sides $AC$ and $AB$ , respectively, such that $\angle ABD = \angle DBC$ and $\angle ACE = \angle ECB$ . Segments $BD$ and $CE$ meet at $I$ .  Determine whether or not it is possible for
segments $AB, AC, BI, ID, CI, IE$ to all have integer lengths.

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Source and history

task_id
281173dc-8b2e-5ae1-ae3f-e72e17ac8291
task_key
test--281173dc-8b2e-5ae1-ae3f-e72e17ac8291
task_revision_id
1
config / split
/ test

Official source

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