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Omni-MATH / Points A,C, and B lie on a line in that order such that AC=4 and BC=2. Circles ω₁,ω₂, and ω₃ have (BC)¯,(AC)¯, and (AB)¯ as diameters. Circle Γ is externally tangent to ω₁ and ω₂ a…

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problem

Points A,CA, C, and BB lie on a line in that order such that AC=4A C=4 and BC=2B C=2. Circles ω1,ω2\omega_{1}, \omega_{2}, and ω3\omega_{3} have BC¯,AC¯\overline{B C}, \overline{A C}, and AB¯\overline{A B} as diameters. Circle Γ\Gamma is externally tangent to ω1\omega_{1} and ω2\omega_{2} at DD and EE respectively, and is internally tangent to ω3\omega_{3}. Compute the circumradius of triangle CDEC D E.
Plain-text mathematical notation (without MathML)
Points A,C, and B lie on a line in that order such that AC=4 and BC=2. Circles ω₁,ω₂, and ω₃ have (BC)¯,(AC)¯, and (AB)¯ as diameters. Circle Γ is externally tangent to ω₁ and ω₂ at D and E respectively, and is internally tangent to ω₃. Compute the circumradius of triangle CDE.
Original LaTeX notation
Points $A, C$, and $B$ lie on a line in that order such that $A C=4$ and $B C=2$. Circles $\omega_{1}, \omega_{2}$, and $\omega_{3}$ have $\overline{B C}, \overline{A C}$, and $\overline{A B}$ as diameters. Circle $\Gamma$ is externally tangent to $\omega_{1}$ and $\omega_{2}$ at $D$ and $E$ respectively, and is internally tangent to $\omega_{3}$. Compute the circumradius of triangle $C D E$.

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Source and history

task_id
5efd9a19-78a9-5cad-9470-1dc634f3f315
task_key
test--5efd9a19-78a9-5cad-9470-1dc634f3f315
task_revision_id
1
config / split
/ test

Official source

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