False. The size of a circle or the location of the intersecting chords does not affect the property observed regarding the sine of an angle. The property that the sine of a specific angle remains the same applies to triangles, not circles or chords.
The concept of sine in trigonometry is specifically related to the ratios of sides in right triangles. It measures the ratio of the length of the side opposite the given angle to the length of the hypotenuse. As such, it does not directly apply to circles or chords.
For circles and chords, properties such as the length of chords, their intersections, and their angles are determined by the properties of the circle, such as its radius or diameter, or the position and geometry of the chords themselves.
Therefore, the property observed regarding the sine of an angle being the same for the same angle in different triangles does not directly apply to circles or chords.