Two chords are congruent if and only if they are equidistant from the center.

1
Theorem 10-4

• Two chords are congruent if and only if they are
  equidistant from the center.

2
Theorem 10-3

• If a diameter or radius is perpendicular to a
  chord, then it bisects the chord and its arc.

3
THEOREM 10-2

• Two minor arcs are congruent if and only if their
  corresponding chords are congruent.

4
THEOREM 10-5

• The measure of the inscribed angle is ½ the
  measure of its intercepted arc.

5
THEOREM 10-6

• If 2 inscribed angles of a circle intercept
  congruent arcs, then the angles are congruent.

6
THEOREM 10-7

• If an inscribed angle intercepts a semicircle,
  the angle is a right angle.

7
THEOREM 10-9

• If a line is tangent to a circle, then it is
  perpendicular to the radius drawn to the point of
  tangency.

8
THEOREM 10-10

• If a line is perpendicular to a radius of a
  circle at its endpoint on the circle, then the
  line is tangent to circle.

9
THEOREM 10-7

• If an inscribed angle intercepts a semicircle,
  the angle is a right angle.

10
THEOREM 10-11

• If two segments from the same exterior point are
  tangent to a circle, then they are congruent.

11
THEOREM 10-12

12
THEOREM 10-13
13
THEOREM 10-14
14
THEOREM 10-14
15
Theorem 10.14
16
Tangent Segments Theorem

• ABAC

17
THEOREM 10-16

• AB(AC)AE(AD)

18
THEOREM 10-17

• WX(WX)WZ(WY)

19
THEOREM 10-15
AE(EC) BE(ED)