Angles in a Circle: Are They Equal?

[Perplexing]

THis is a rather simple question and please feel free to delete it after it has been answered.

I know that in a circle, Angles Subtended by the same Segment are equal. Question: Are angles subtended by equal, yet different (different positions on the circle), euqal?

Thanks

 

[Curious3141]

You mean drawing another chord of the same length and seeing what you get for the angle subtended ? It should be, since the shapes can be rotated and superimposed perfectly (that is, the figures are congruent).

 

[tacman]

for your question. Yes, angles subtended by equal, yet different positions on a circle are equal. This is known as the angle subtended by a chord theorem, which states that if two chords in a circle are equal in length, then the angles subtended by those chords at the center of the circle are also equal. This applies to any position on the circle, as long as the chords are equal in length. So, in short, all angles in a circle are equal if they are subtended by equal chords. I hope this helps clarify the concept of angles in a circle for you.