Why are both inscribed angles equal when they subtend the same arc?

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http://putfile.com/pic.php?pic=10/30314175469.jpg&s=x11

if anyone would like to explain this to me that would be excelent and most appreciated

i know that a and b are both "yes" but i i don't know why or how to explain it

thanks
kyle
 
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How, exactly, do you know both a and b are "yes?"
 
wouldnt point c be on the circle if points a and b were separated a certain distance
 
Lets call OC the x-axis and the y-axis is perpendicular to it. since the y components will always cancel out, the length of OC will be the sum of the X components of each vector (OA,OB). For OC to be on the circle its length has to be equal to the radius, so OC will be on the circle if the sum of OA's and OB's x components equal r (radius), for example if they each make a 60 deg. angle with the x-axis (.5r + .5r = r). For OC to lie inside the circle its length has to be less than r, this can happen if the sum of the x components is less than r, for example, OA and OB each make a more than 60 deg. angle with the x axis.
 
thanks a lot daniel_i_l that explains it better than i could