Do Equal Angles at the Circumference Subtend Equal Chords? Do Equal Angles at the Circumference Subtend Equal Chords? This may seem like a pretty basic question but I can't seem to find a definite answer on the internet and none of my textbooks mention this rule. Is this rule correct?

It is true that equal angles at circumference subtend equal chords.

However, the explanation should NOT be taken as the chord length is proportional to the angle subtended at circumference.

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In the figure, all green marked angles are equal. Then $\dfrac {L}{2} = r \sin \theta$. After simplification (by treating r as constant), we have $\quad L \quad \alpha \quad \sin \theta \quad$ .