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Omni-MATH / In quadrilateral ABCD, there exists a point E on segment AD such that (AE)/(ED)=(1)/(9) and ∠BEC is a right angle. Additionally, the area of triangle CED is 27 times more than the …

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problem

In quadrilateral ABCDABCD, there exists a point EE on segment ADAD such that AEED=19\frac{AE}{ED}=\frac{1}{9} and ∠BEC\angle BEC is a right angle. Additionally, the area of triangle CEDCED is 27 times more than the area of triangle AEBAEB. If ∠EBC=∠EAB,∠ECB=∠EDC\angle EBC=\angle EAB, \angle ECB=\angle EDC, and BC=6BC=6, compute the value of AD2AD^{2}.
Plain-text mathematical notation (without MathML)
In quadrilateral ABCD, there exists a point E on segment AD such that (AE)/(ED)=(1)/(9) and ∠BEC is a right angle. Additionally, the area of triangle CED is 27 times more than the area of triangle AEB. If ∠EBC=∠EAB,∠ECB=∠EDC, and BC=6, compute the value of AD².
Original LaTeX notation
In quadrilateral $ABCD$, there exists a point $E$ on segment $AD$ such that $\frac{AE}{ED}=\frac{1}{9}$ and $\angle BEC$ is a right angle. Additionally, the area of triangle $CED$ is 27 times more than the area of triangle $AEB$. If $\angle EBC=\angle EAB, \angle ECB=\angle EDC$, and $BC=6$, compute the value of $AD^{2}$.

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Source and history

task_id
acb95315-c771-5011-b108-bae45d469169
task_key
test--acb95315-c771-5011-b108-bae45d469169
task_revision_id
1
config / split
/ test

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