Angles in Circles -- A Summary
by David Pleacher

Types of Angles

1. central angle = arc
2. angle formed by radius and tangent = 90°
3. inscribed angle = 1/2 arc
4. angle formed by tangent and chord = 1/2 arc
5. angle formed by 2 lines intersecting inside a circle = 1/2 of the sum of the 2 intercepted arcs
6. angle formed by 2 lines intersecting outside a circle = 1/2 of the difference of the 2 arcs

Important postulates, definitions, and theorems

1. All radii of a circle are congruent.
2. If a radius is perpendicular to a chord, then it bisects it.   (converse is also true)
3. If 2 arcs of a circle are congruent, then the chords are congruent.
   (converse is also true)
4. If 2 chords are equidistant from the center of a circle, then they are congruent.
   (converse is also true)
5. If a radius bisects a chord, then it bisects its arc.   (converse is also true)
6. An angle inscribed in a semicircle is a right angle.
7. Tangent segments to a circle are congruent.
8. A radius is perpendicular to a tangent.
9. If two chords intersect inside a circle, the products of their segments are equal.
   

Send any comments or questions to: David Pleacher