Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: In a circle with center $O$, $AD$ is a diameter, $ABC$ is a chord, $BO = 5$, and $\angle ABO = \text{arc } CD = 60^\circ$.  Find the length of $BC$.

[asy]
import graph;

unitsize(2 cm);

pair O, A, B, C, D;

O = (0,0);
A = dir(30);
C = dir(160);
B = (2*C + A)/3;
D = -A;

draw(Circle(O,1));
draw(C--A--D);
draw(B--O);

label("$A$", A, NE);
label("$B$", B, N);
label("$C$", C, W);
label("$D$", D, SW);
label("$O$", O, SE);
[/asy]
user