Length of Chord of Circle/Proof 2

Proof
We have $AO = BO$ since they are radii.

Therefore $\triangle AOB$ is isosceles.

By Isosceles Triangle has Two Equal Angles:


 * $\angle OAB = \angle OBA$

By Sum of Angles of Triangle equals Two Right Angles:


 * $\angle OAB + \angle OBA + \theta = 180 \degrees$

Therefore $\angle OAB = \dfrac {180 \degrees - \theta} 2 = 90 \degrees - \dfrac \theta 2$.

Thus: