@TSS-Graviser That's a good question; it depends on what you mean by meaningful! The line segments happen to be the side lengths of the triangles in the picture. Maybe you will see a math question that asks for one of the lengths of the triangles. In that case, knowing Power of a Point will be very meaningful!
The yellow arc goes with the yellow angle. The yellow angle is inscribed inside the yellow arc. That means that the yellow angle's measure is \( \frac{1}{2}\) of the measure of the arc.
So to answer your emailed question, 🙂 , suppose an angle opens up to exactly half of the circle. That half of the circle is an arc with measure \( 180^{\circ}.\) That means the angle is \( 90^{\circ}.\)