Theorems to try to prove next:

1. Prove that for any inscribed angle, the measure of the inscribed angle is half of the measure of the central angle that intercepts the same arc.

Note: We have proved this for the case where the one side of the inscribed angle is a diameter, and the case where the center lies in the interior of the inscribed angle, which leaves to be proven only the case where the interior of the inscribed angle does not contain the center.

2. Prove that the segment that connects the centers of two externally tangent circles* passes through the point of tangency.

*Two circles are externally tangent if they intersect in exactly one point, and if neither center lies in the interior of the other circle.