# Math Help - Angle sbutended by a chord in a circle

1. ## 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:

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?