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Omni-MATH / Let ABCD be a trapezoid with AB∥CD and ∠D=90^(∘). Suppose that there is a point E on CD such that AE=BE and that triangles AED and CEB are similar, but not congruent. Given that …

Problem

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problem

Let ABCDABCD be a trapezoid with AB∥CDAB \parallel CD and ∠D=90∘\angle D=90^{\circ}. Suppose that there is a point EE on CDCD such that AE=BEAE=BE and that triangles AEDAED and CEBCEB are similar, but not congruent. Given that CDAB=2014\frac{CD}{AB}=2014, find BCAD\frac{BC}{AD}.
Plain-text mathematical notation (without MathML)
Let ABCD be a trapezoid with AB∥CD and ∠D=90^(∘). Suppose that there is a point E on CD such that AE=BE and that triangles AED and CEB are similar, but not congruent. Given that (CD)/(AB)=2014, find (BC)/(AD).
Original LaTeX notation
Let $ABCD$ be a trapezoid with $AB \parallel CD$ and $\angle D=90^{\circ}$. Suppose that there is a point $E$ on $CD$ such that $AE=BE$ and that triangles $AED$ and $CEB$ are similar, but not congruent. Given that $\frac{CD}{AB}=2014$, find $\frac{BC}{AD}$.

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Source and history

task_id
803abcee-bf8b-5c39-8184-6ab08bf2d71e
task_key
test--803abcee-bf8b-5c39-8184-6ab08bf2d71e
task_revision_id
1
config / split
/ test

Official source

initial import