THEOREMS ON CIRCLE

• Theorem 1

  In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent
• Theorem 2

  In a circle or in a congruent circle, two minor arcs are congruent if and only if their corresponding chords are congruent
• Theorem 3

  In a circle, a diameter bisects an arc with the same endpoints if and only if it's perpendicular to the chord
• Theorem 4

  In the same circle or in congruent circles, chords equidistant from the center are congruent
• Theorem 5

  In the same circle or in congruent circles, any two congruent arcs are equidistant from the center
• Arc Addition Postulate

  The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs
• Sector of a circle

  The region bounded by an arc of the circle and the radii to the endpoints of the arc
• Finding the area of a sector

  Multiply the ratio of the arc measure to 360 degrees by the area of the circle
• Segment of a circle

  The region bounded by an arc and the chord joining its endpoints
• Finding the area of a segment

  Subtract the area of the triangle formed by the chord and radii from the area of the sector