center is point , choose three points on the circle. Draw lines and : angle is an inscribed angle. Now draw line and extend it past point so that it intersects the circle at point . Angle intercepts arc on the circle.

Suppose this arc does not include point within it. Point is diametrically opposite to point . Angles are also inscribed angles, but both of these angles have one side which passes through the center of the circle, therefore the theorem from the above Part 1 can be applied to them.

Therefore,

then

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