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]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4\pi - 2\sqrt{3}
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]
train