Central and inscribed angles in a circle
Euclid enumerates several propositions about a circle, for example:
III.20. In a circle the angle at the center is double the angle at the circunference, when the rays forming the angles meet the circunference in the same two points.
III.21. In a circle, a chord subtends equal angles at any two points on the same one of the two arcs determined by the chord.
III.32. If a chord of a circle be drawn from the point of contact of a tangent, the angle made by the chord with the tangent is equal to the angle subtended by the chord at a point on that part of the circunference which lies on the far side of the chord.
In the applet these properties are shown. Points can be moved to see different configurations.
The base of these results is "pons asinorum", that is to say, that the angles of the base of an isosceles triangle are equal.
We can see several "monstrations" that illustrate different passages from the demonstration of this property.
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