# Angle sbutended by a chord in a circle

• Sep 10th 2010, 09:00 AM
ankush
Angle sbutended by a chord in a circle
I was going through the proof of a theorem which says, "The angle subtended by a chord at the center of a circle is twice the angle subtended by it elsewhere on the circle."

This was proved by considering three cases: when the arc forming the chord was:
1) a minor arc
2) a major arc
3) a semi circle

I realized that the following scenario has been avoided, which is what I'm trying to prove:

Attachment 18877

Prove that: Angle AOB = 2 * Angle APB

You see, the textbook very cleverly takes the point P above the point O, which allows joining O and P, and the problem is easily solved by using the property of exterior angles.

Is this interpretation right? If not, why? If yes, how is it to be proved?

• Sep 10th 2010, 09:27 AM
masters
Hi ankush,

Check this out: Inscribed-Central Angle Proof
• Sep 10th 2010, 09:32 AM
ankush
Well, thank you, but this has already been covered in the book. Besides, the animation you provided talks about an arc, not a chord (though it works out to be the same thing).

Could you please comment on the figure I posted?