Quizlet Chapter 9 theorems

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  1. a chord that contains the center of a circle: Diameter
  2. A diameter that is perpendicular to a chord bisects the chord and its arc: A diameter that is perpendicular to a chord bisects the chord and its arc
  3. a line that contains a chord: Secant
  4. A line that is tangent to each of two coplanar circles: Common tangent
  5. a set of points in a plane at a given distance from a given point in that plane: Circle
  6. An angle inscribed in a semicircle is a right angle: An angle inscribed in a semicircle is a right angle
  7. an angle whose vertex is on a circle and whose sides contain chords of the circle: Inscribed angle
  8. angle with its vertex at the center of a circle: Central angle
  9. circles that have congruent radii: Congruent circles
  10. circles that lie in the same plane and have the same center: Concentric circles
  11. If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle: If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle
  12. If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency
  13. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
  14. If two inscribed angles intercept the same arc, then the angles are congruent: If two inscribed angles intercept the same arc, then the angles are congruent
  15. In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent: In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent
  16. In the same circle or in congruent circles: Chords equally distant from the center are congruent: In the same circle or in congruent circles: Chords equally distant from the center are congruent
  17. In the same circle or in congruent circles: congruent arcs have congruent chords: In the same circle or in congruent circles: congruent arcs have congruent chords
  18. In the same circle or in congruent circles: Congruent chords are equally distant from the center: In the same circle or in congruent circles: Congruent chords are equally distant from the center
  19. In the same circle or in congruent circles: Congruent chords have congruent arcs: In the same circle or in congruent circles: Congruent chords have congruent arcs
  20. line in the plane of a circle that intersects the circle in exactly one point: Tangent
  21. segment whose endpoints lie on a circle: Chord
  22. set of all points in a space at a distance: Sphere
  23. sphere that have the same center: Concentric spheres
  24. spheres that have congruent radii: Congruent spheres
  25. Tangents to a circle from a point are congruent: Tangents to a circle from a point are congruent
  26. the given distance: Radius
  27. the given point of the circle: Center
  28. The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc: The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc
  29. The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs: The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs
  30. The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs
  31. The measure of an inscribed angle is equal to half the measure of its intercepted arc: The measure of an inscribed angle is equal to half the measure of its intercepted arc
  32. The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs: Arc Addition Postulate
  33. When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment: When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment
  34. When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord: When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord
  35. When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment: When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment