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Omni-MATH / A semicircle with radius 2021 has diameter AB and center O. Points C and D lie on the semicircle such that ∠AOC<∠AOD=90^(∘). A circle of radius r is inscribed in the sector bounded…

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problem

A semicircle with radius 2021 has diameter ABAB and center OO. Points CC and DD lie on the semicircle such that ∠AOC<∠AOD=90∘\angle AOC < \angle AOD = 90^{\circ}. A circle of radius rr is inscribed in the sector bounded by OAOA and OCOC and is tangent to the semicircle at EE. If CD=CECD=CE, compute ⌊r⌋\lfloor r \rfloor.
Plain-text mathematical notation (without MathML)
A semicircle with radius 2021 has diameter AB and center O. Points C and D lie on the semicircle such that ∠AOC<∠AOD=90^(∘). A circle of radius r is inscribed in the sector bounded by OA and OC and is tangent to the semicircle at E. If CD=CE, compute ⌊r⌋.
Original LaTeX notation
A semicircle with radius 2021 has diameter $AB$ and center $O$. Points $C$ and $D$ lie on the semicircle such that $\angle AOC < \angle AOD = 90^{\circ}$. A circle of radius $r$ is inscribed in the sector bounded by $OA$ and $OC$ and is tangent to the semicircle at $E$. If $CD=CE$, compute $\lfloor r \rfloor$.

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Source and history

task_id
b3e4a211-9c96-552e-ab75-aa25f8dd6f95
task_key
test--b3e4a211-9c96-552e-ab75-aa25f8dd6f95
task_revision_id
1
config / split
/ test

Official source

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