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Omni-MATH / An isosceles trapezoid ABCD with bases AB and CD has AB=13,CD=17, and height 3. Let E be the intersection of AC and BD. Circles Ω and ω are circumscribed about triangles ABE and …

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problem

An isosceles trapezoid ABCDA B C D with bases ABA B and CDC D has AB=13,CD=17A B=13, C D=17, and height 3. Let EE be the intersection of ACA C and BDB D. Circles Ω\Omega and ω\omega are circumscribed about triangles ABEA B E and CDEC D E. Compute the sum of the radii of Ω\Omega and ω\omega.
Plain-text mathematical notation (without MathML)
An isosceles trapezoid ABCD with bases AB and CD has AB=13,CD=17, and height 3. Let E be the intersection of AC and BD. Circles Ω and ω are circumscribed about triangles ABE and CDE. Compute the sum of the radii of Ω and ω.
Original LaTeX notation
An isosceles trapezoid $A B C D$ with bases $A B$ and $C D$ has $A B=13, C D=17$, and height 3. Let $E$ be the intersection of $A C$ and $B D$. Circles $\Omega$ and $\omega$ are circumscribed about triangles $A B E$ and $C D E$. Compute the sum of the radii of $\Omega$ and $\omega$.

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Source and history

task_id
5c64a545-ca77-5efc-aae5-de5b63a714ca
task_key
test--5c64a545-ca77-5efc-aae5-de5b63a714ca
task_revision_id
1
config / split
/ test

Official source

initial import