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Geometry
Chapter 9
The following is a list of items you need to know for the test.
 circle
 concentric circles and spheres
 center
 inscribed polygons / circumscribed circles
chord
 radius
 inscribed circles / circumscribed polygons
 chord
 common tangents
diameter
 secant
 tangent circles

 diameter
 central angles
radius
secant
 tangent
 minor arc
 point of tangency
 major arc
 sphere
 semicircle
tangent
 congruent circles
 inscribed angles
Theorems
 If a line is tangent to a circle, then the line is  to the radius drawn to the point of tangency.
 If a line is  to a radius at its outer endpoint, then the line is tangent to the circle.
 Minor arcs are  if and only if their central angles are  .
 In the same circle or in  circles:
(1)  arcs have  chords.
(2)  chords have  arcs.
 A diameter that is  to a chord, bisects the chord and its arc.
 In the same circle or in  circles:
(1) chords equally distant from the center are  .
(2)  chords are equally distant form the center.
 An inscribed  = ½ its intercepted arc.
 The  formed by a chord and a tangent = ½ its intercepted arc.
 The  formed by 2 chords that intersect inside a circle = ½ the sum of the intercepted arcs.
 The  formed by 2 secants, 2 tangents, or a secant and a tangent = ½ the difference of the intercepted
arcs.
 When 2 chords intersect inside a circle, the product of the segments of 1 chord = the product of the
segments of the other chord. (part X part = part X part)
 The product of one secant and its external segment = the product of the other secant and its external
segment. (outside X total = outside X total)
 The product of one secant and its external segment = the square of the tangent. (outside X total =
outside X total)
Corollaries
 Tangents to a circle from a point are  .
 If 2 inscribed  s intercept the same arc, then the angles are  .
 An  inscribed in a semicircle is a right  .
 If a quadrilateral is inscribed in a semicircle, then its opposite  s are supplementary.
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