The problem shown in the image involves calculating the arc lengths of segments AB, AC, BD, and CD of a circle, where the center of the circle is marked $O$. The central angles given are:

• $\angle AOB = 60^\circ$
• $\angle AOC = 150^\circ$
• $\angle BOC = 90^\circ$

To solve this, we need the radius $r$ of the circle and will use the formula for arc length $s$:

$s = \theta \times \frac{\pi r}{180}$

where $\theta$ is the central angle in degrees, and $r$ is the radius of the circle.

Let's address the arcs based on the angles provided:

• Arc AB corresponds to $\angle AOB = 60^\circ$
• Arc AC corresponds to $\angle AOC = 150^\circ$
• Arc BD corresponds to $\angle BOD = \text{(should be the remaining angle based on full 360°)}$
• Arc CD will need the angle of the remaining section of the circle as well.

Could you please confirm if the radius $r$ of the circle is provided or would you like to assume a value to proceed with the calculations?

Once I know the radius, I'll calculate the arc lengths for each section.