Angles in Circles
The relationship between angles and the circle is very important in the study of geometry. Several topics related to astronomy are strictly related to the study of the angles inside or outside the circle and their properties. There are Central Angles, Inscribed Angles, Exterior Angles, Interior Angles and Tangent Chord Angles. In the following table guide you can see its main characteristics:
| Name | Image | Description |
|---|---|---|
| Central Angle |  | A central angle is an angle formed by two radii with the vertex at the center of the circle. The measure of the central angle is the same as the measure of the arc that the two sides cut out of the circle, specifically, `A hat(0) B = hat(AB)`. |
| Inscribed Angle |  | An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords. The measure of the inscribed angle is half that of the arc that the two sides cut out of the circle, specifically, `A hat(0) B = (hat(AB))/2`. |
| Exterior Angle |  | An exterior angle has its vertex where two rays share an endpoint outside a circle. The sides of the angle are those two rays. The measure of an exterior angle is found by the following formula: `A hat(0) B = (hat(AB) - hat(CD))/2`. |
| Interior Angle |  | An interior angle has its vertex at the intersection of two lines that intersect inside a circle. The sides of the angle lie on the intersecting lines. The measure of an interior angle can be found by the following formula: `A hat(0) B = (hat(AB) + hat(CD))/2`. |
| Tangent Chord Angle |  | An angle formed by an intersecting tangent and chord has its vertex "on" the circle. The measure of an tangent chord angle is found by the following formula: `A hat(0) B = (hat(AO))/2`. |
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