Proving Angles in a Circle: Angle 2 is Twice Angle 1

[Vashti]

http://s14.photobucket.com/albums/a348/Drakhys-2/?action=view&current=scan.jpg

How would I prove that angle 2 is twice the size of angle 1?


thankyou,
Vash.

 

[Curious3141]

Hint : join the center to the peripheral point with a line segment. Let that line segment divide angle 1 into two (not necessarily equal) angles alpha and beta. Now observe the two isoceles triangles formed by the dividing line segment. By considering angle sums, find the angle in each triangle that is subtended at the center of the circle. Now using the angle sum about a point, find angle 2 in terms of alpha and beta, and hence angle 1.

 

[Tide]

If the two chords from the top point are of equal length (?) then can you see that 2(pi -angle 1) + angle 2 must equal 2 pi?