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MATH / In the figure, square WXYZ has a diagonal of 12 units. Point A is a midpoint of segment WX, segment AB is perpendicular to segment AC and AB=AC. What is the length of segment BC? […

Problem

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problem

In the figure, square WXYZWXYZ has a diagonal of 12 units. Point AA is a midpoint of segment WXWX, segment ABAB is perpendicular to segment ACAC and AB=AC.AB = AC. What is the length of segment BCBC? [asy] import olympiad; size(150); defaultpen(linewidth(0.8)); draw(unitsquare); draw((2,0)--(0.5,0)--(0.5,1.5)--cycle); label("WW",(0,0),W); label("XX",(1,0),S); label("YY",(1,1),E); label("ZZ",(0,1),W); label("AA",(0.5,0),S); label("BB",(2,0),E); label("CC",(0.5,1.5),N); [/asy]
Plain-text mathematical notation (without MathML)
In the figure, square WXYZ has a diagonal of 12 units. Point A is a midpoint of segment WX, segment AB is perpendicular to segment AC and AB=AC. What is the length of segment BC? [asy]
import olympiad; size(150); defaultpen(linewidth(0.8));

draw(unitsquare);
draw((2,0)--(0.5,0)--(0.5,1.5)--cycle);
label("W",(0,0),W); label("X",(1,0),S); label("Y",(1,1),E); label("Z",(0,1),W);
label("A",(0.5,0),S); label("B",(2,0),E); label("C",(0.5,1.5),N);
[/asy]
Original LaTeX notation
In the figure, square $WXYZ$ has a diagonal of 12 units. Point $A$ is a midpoint of segment $WX$, segment $AB$ is perpendicular to segment $AC$ and $AB = AC.$ What is the length of segment $BC$? [asy]
import olympiad; size(150); defaultpen(linewidth(0.8));

draw(unitsquare);
draw((2,0)--(0.5,0)--(0.5,1.5)--cycle);
label("$W$",(0,0),W); label("$X$",(1,0),S); label("$Y$",(1,1),E); label("$Z$",(0,1),W);
label("$A$",(0.5,0),S); label("$B$",(2,0),E); label("$C$",(0.5,1.5),N);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
695b64f3-2247-5373-b60a-09c8a92f4c7a
task_key
geometry--test--695b64f3-2247-5373-b60a-09c8a92f4c7a
task_revision_id
1
config / split
geometry / test

Official source

initial import