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MATH / Rectangle ABCD has center O and AB/AD=k. A point is randomly chosen from the interior of rectangle ABCD. What is the probability that it is closer to O than to any of the four vert…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Rectangle ABCDABCD has center OO and AB/AD=kAB/AD=k. A point is randomly chosen from the interior of rectangle ABCDABCD. What is the probability that it is closer to OO than to any of the four vertices? [asy] size(200); draw((-250,100)--(250,100)--(250,-100)--(-250,-100)--cycle); dot((0,0)); label("OO",(0,0),N); label("AA",(-250,100),NW); label("BB",(250,100),NE); label("CC",(250,-100),SE); label("DD",(-250,-100),SW);[/asy]
Plain-text mathematical notation (without MathML)
Rectangle ABCD has center O and AB/AD=k. A point is randomly chosen from the interior of rectangle ABCD. What is the probability that it is closer to O than to any of the four vertices?  [asy]
size(200);
draw((-250,100)--(250,100)--(250,-100)--(-250,-100)--cycle);
dot((0,0));
label("O",(0,0),N);
label("A",(-250,100),NW); label("B",(250,100),NE); label("C",(250,-100),SE); label("D",(-250,-100),SW);[/asy]
Original LaTeX notation
Rectangle $ABCD$ has center $O$ and $AB/AD=k$. A point is randomly chosen from the interior of rectangle $ABCD$. What is the probability that it is closer to $O$ than to any of the four vertices?  [asy]
size(200);
draw((-250,100)--(250,100)--(250,-100)--(-250,-100)--cycle);
dot((0,0));
label("$O$",(0,0),N);
label("$A$",(-250,100),NW); label("$B$",(250,100),NE); label("$C$",(250,-100),SE); label("$D$",(-250,-100),SW);[/asy]

level

Level 5

type

Counting & Probability

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Source and history

task_id
31065225-b9a3-5a77-8757-ff106340ddcf
task_key
counting~5fand~5fprobability--test--31065225-b9a3-5a77-8757-ff106340ddcf
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import