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MATH / The area of the semicircle in Figure A is half the area of the circle in Figure…

Problem

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

problem

The area of the semicircle in Figure A is half the area of the circle in Figure B. The area of a square inscribed in the semicircle, as shown, is what fraction of the area of a square inscribed in the circle? Express your answer as a common fraction.

[asy]
defaultpen(linewidth(0.8));

size(5cm,5cm);

draw((0,0)..(1,1)..(2,0)--(0,0));

draw((0.5,0)--(0.5,0.87)--(1.5,0.87)--(1.5,0));

draw(Circle((4,0),1));

pair A,B,C,D;

A=(3.3,0.7);
B=(3.3,-0.7);
D=(4.7,0.7);
C=(4.7,-0.7);

draw(A--B--C--D--A);

label("Figure A",(1,1.3));
label("Figure B",(4,1.3));

[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
b5bdddfe-fd42-529f-8667-449ae398eb60
task_key
geometry--test--b5bdddfe-fd42-529f-8667-449ae398eb60
task_revision_id
1
config / split
geometry / test

Official source

initial import