I have recently came across the "Secant Interior Angle Theorem." An image of this is at this link: http://i.imgur.com/i12awai.png . I have been trying to think of a proof to this theorem, but no matter what approach I try, I can not think of a proof. Please help me if you can by explaining to me the proof for this theorem. Thanks in advance. Sorry for any grammar/spelling/etc. errors.

Question

anonymous · Answer

@e.mccormick Any ideas, please?

anonymous · Answer

@jigglypuff314

e.mccormick · Answer

Did you try making lines through BN and DM?  It will intersect and make some triangles.

anonymous · Answer

I did think about doing that, but those line segments BN and DM wouldn't be related to their arc measurements, would they?

e.mccormick · Answer

There is  a relationship there.  The is the relationship of the area and the arc segment to the points on the circle.

anonymous · Answer

Sorry, but I don't exactly get what you're saying. Can you attach a drawing or something of the sort so I can visualize it?

e.mccormick · Answer

Have you looked at the Intersecting Chord Theorem and proofs for it?  There are a few different ways to take it on.

e.mccormick · Answer

If you can prove hings about the lines and triangles involved, then you should be able to go from there to the angles. Or at least that is my thoughts on it. http://www.cut-the-knot.org/proofs/IntersectingChordsTheorem.shtml http://www.proofwiki.org/wiki/Intersecting_Chord_Theorem

anonymous · Answer

OK, I think I have an idea of how to prove it based off of those websites. Thank you so much! This problem has been bothering me for a while.

e.mccormick · Answer

Yah, that proof is related to what you want to prove.  Once you have the angles proven, then the relationship between the arcs and the chords is the bridge to what you want.