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Omni-MATH / Let ω be a circle, and let ABCD be a quadrilateral inscribed in ω. Suppose that BD and AC intersect at a point E. The tangent to ω at B meets line AC at a point F, so that C lies b…

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problem

Let ω\omega be a circle, and let ABCDABCD be a quadrilateral inscribed in ω\omega. Suppose that BDBD and ACAC intersect at a point EE. The tangent to ω\omega at BB meets line ACAC at a point FF, so that CC lies between EE and FF. Given that AE=6,EC=4,BE=2AE=6, EC=4, BE=2, and BF=12BF=12, find DADA.
Plain-text mathematical notation (without MathML)
Let ω be a circle, and let ABCD be a quadrilateral inscribed in ω. Suppose that BD and AC intersect at a point E. The tangent to ω at B meets line AC at a point F, so that C lies between E and F. Given that AE=6,EC=4,BE=2, and BF=12, find DA.
Original LaTeX notation
Let $\omega$ be a circle, and let $ABCD$ be a quadrilateral inscribed in $\omega$. Suppose that $BD$ and $AC$ intersect at a point $E$. The tangent to $\omega$ at $B$ meets line $AC$ at a point $F$, so that $C$ lies between $E$ and $F$. Given that $AE=6, EC=4, BE=2$, and $BF=12$, find $DA$.

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Source and history

task_id
0e149ea2-05b1-5f22-bd1a-fe474c6a1033
task_key
test--0e149ea2-05b1-5f22-bd1a-fe474c6a1033
task_revision_id
1
config / split
/ test

Official source

initial import