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MATH / A plane contains points A and B with AB=1. Let S be the union of all disks of radius 1 in the plane that cover (AB)¯. What is the area of S? Express your answer in terms of π and i…

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problem

A plane contains points AA and BB with AB=1AB = 1. Let SS be the union of all disks of radius 1 in the plane that cover AB¯\overline{AB}. What is the area of SS? Express your answer in terms of π\pi and in simplest radical form.
Plain-text mathematical notation (without MathML)
A plane contains points A and B with AB=1.  Let S be the union of all disks of radius 1 in the plane that cover (AB)¯. What is the area of S? Express your answer in terms of π and in simplest radical form.
Original LaTeX notation
A plane contains points $A$ and $B$ with $AB = 1$.  Let $S$ be the union of all disks of radius 1 in the plane that cover $\overline{AB}$. What is the area of $S$? Express your answer in terms of $\pi$ and in simplest radical form.

level

Level 5

type

Geometry

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Source and history

task_id
98bece5d-d77b-5d84-b4b5-a0159f710af5
task_key
geometry--test--98bece5d-d77b-5d84-b4b5-a0159f710af5
task_revision_id
1
config / split
geometry / test

Official source

initial import