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MATH / Segment AB measures 4 cm and is a diameter of circle P. In triangle ABC, point C is on circle P and BC=2 cm. What is the area of the shaded region? [asy] import graph; fill(Circle(…

Problem

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

problem

Segment ABAB measures 4 cm and is a diameter of circle PP. In triangle ABCABC, point CC is on circle PP and BC=2BC = 2 cm. What is the area of the shaded region? [asy] import graph; fill(Circle((0,0),20),gray(0.7)); draw(Circle((0,0),20)); draw((-16,12)--(16,-12)--(0,-20)--cycle); fill((-16,12)--(16,-12)--(0,-20)--cycle,white); label("AA",(-16,12),NW); label("BB",(16,-12),SE); label("CC",(0,-20),S); label("PP",(0,0),N); dot((-16,12)); dot((16,-12)); dot((0,0)); dot((0,-20)); [/asy]
Plain-text mathematical notation (without MathML)
Segment AB measures 4 cm and is a diameter of circle P. In triangle ABC, point C is on circle P and BC=2 cm. What is the area of the shaded region?

[asy]
import graph;
fill(Circle((0,0),20),gray(0.7));
draw(Circle((0,0),20));
draw((-16,12)--(16,-12)--(0,-20)--cycle);
fill((-16,12)--(16,-12)--(0,-20)--cycle,white);
label("A",(-16,12),NW);
label("B",(16,-12),SE);
label("C",(0,-20),S);
label("P",(0,0),N);
dot((-16,12));
dot((16,-12));
dot((0,0));
dot((0,-20));
[/asy]
Original LaTeX notation
Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 2$ cm. What is the area of the shaded region?

[asy]
import graph;
fill(Circle((0,0),20),gray(0.7));
draw(Circle((0,0),20));
draw((-16,12)--(16,-12)--(0,-20)--cycle);
fill((-16,12)--(16,-12)--(0,-20)--cycle,white);
label("$A$",(-16,12),NW);
label("$B$",(16,-12),SE);
label("$C$",(0,-20),S);
label("$P$",(0,0),N);
dot((-16,12));
dot((16,-12));
dot((0,0));
dot((0,-20));
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
f2c9ae1c-2c59-5bdf-9741-235f935d2ebe
task_key
geometry--test--f2c9ae1c-2c59-5bdf-9741-235f935d2ebe
task_revision_id
1
config / split
geometry / test

Official source

initial import