Tangent Thorems -
Theorem 10.1: In a plane, a line is a tangent to a circle if and only if the line is perpendicular to a radius of a circle at its endpoint on the circle.
Theorem 10.2: Tangent segments that form a common external point are congruent.
Chord Theorems -
Theorem 10.3: In the same circe or in congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent.
Theorem 10.4: If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
Theorem 10.5:If a diameter of a circle is perpendicular to a chord then the diameter bisects the chord and it arc.
Theorem 10.6: In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from its center.
Theorem 10.7:The measure of a inscribed angle is half the measure of its intercepted arc is an angle whose vertex is on a circle and whose sides contain chords.
Theorem 10.8:If 2 inscribed angles of a circle intercept the same arc, then the angles are congruent.
Theorem 10.9: If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of a circle. Conversely, if one side of and inscribed triangle is a diameter of the circle then the triangle is a right triangle and the angle opposite to the diameter is a right angle.
Theorem 10.10: A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Congruent Arcs: Two arcs are congruent if they have the same measure and they are acrs of the same circle or of congruent circles.