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Omni-MATH / Equilateral △ABC has side length 6. Let ω be the circle through A and B such that CA and CB are both tangent to ω. A point D on ω satisfies CD=4. Let E be the intersection of line …

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problem

Equilateral △ABC\triangle A B C has side length 6. Let ω\omega be the circle through AA and BB such that CAC A and CBC B are both tangent to ω\omega. A point DD on ω\omega satisfies CD=4C D=4. Let EE be the intersection of line CDC D with segment ABA B. What is the length of segment DED E?
Plain-text mathematical notation (without MathML)
Equilateral △ABC has side length 6. Let ω be the circle through A and B such that CA and CB are both tangent to ω. A point D on ω satisfies CD=4. Let E be the intersection of line CD with segment AB. What is the length of segment DE?
Original LaTeX notation
Equilateral $\triangle A B C$ has side length 6. Let $\omega$ be the circle through $A$ and $B$ such that $C A$ and $C B$ are both tangent to $\omega$. A point $D$ on $\omega$ satisfies $C D=4$. Let $E$ be the intersection of line $C D$ with segment $A B$. What is the length of segment $D E$?

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task_id
4e010329-9ce8-58be-b8ad-d8a4b59f833d
task_key
test--4e010329-9ce8-58be-b8ad-d8a4b59f833d
task_revision_id
1
config / split
/ test

Official source

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