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MATH / In the circle below, (AB)¯‖(CD)¯. (AD)¯ is a diameter of the circle, and AD = 36^{prime prime}. What is the number of inches in the length of (AB)^? Express your answer in terms of…

Problem

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

problem

In the circle below, AB¯‖CD¯\overline{AB} \| \overline{CD}. AD¯\overline{AD} is a diameter of the circle, and $AD = 36^{\prime \prime}$. What is the number of inches in the length of AB^\widehat{AB}? Express your answer in terms of π\pi. [asy] import markers; import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8)); draw(Circle(origin,36)); pair A = 36*dir(130); pair B = 36*dir(50); pair D = 36*dir(-50); pair C = 36*dir(-130); draw(B--A--D--C); label("AA",A,W); label("BB",B,E); label("CC",C,W); label("DD",D,E); markangle("50∘50^{\circ}",D,A,B,radius=10); [/asy]
Plain-text mathematical notation (without MathML)
In the circle below, (AB)¯‖(CD)¯. (AD)¯ is a diameter of the circle, and $AD = 36^{\prime \prime}$. What is the number of inches in the length of (AB)^? Express your answer in terms of π. [asy]
import markers;
import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8));
draw(Circle(origin,36));
pair A = 36*dir(130);
pair B = 36*dir(50);
pair D = 36*dir(-50);
pair C = 36*dir(-130);
draw(B--A--D--C);
label("A",A,W); label("B",B,E); label("C",C,W); label("D",D,E);
markangle("50^(∘)",D,A,B,radius=10);
[/asy]
Original LaTeX notation
In the circle below, $\overline{AB} \| \overline{CD}$. $\overline{AD}$ is a diameter of the circle, and $AD = 36^{\prime \prime}$. What is the number of inches in the length of $\widehat{AB}$? Express your answer in terms of $\pi$. [asy]
import markers;
import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8));
draw(Circle(origin,36));
pair A = 36*dir(130);
pair B = 36*dir(50);
pair D = 36*dir(-50);
pair C = 36*dir(-130);
draw(B--A--D--C);
label("$A$",A,W); label("$B$",B,E); label("$C$",C,W); label("$D$",D,E);
markangle("$50^{\circ}$",D,A,B,radius=10);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
69c40072-cb69-5cad-8446-2f52fb79d06d
task_key
geometry--test--69c40072-cb69-5cad-8446-2f52fb79d06d
task_revision_id
1
config / split
geometry / test

Official source

initial import