• • Corollary 3

    The opposite angles of a quadrilateral inscribed in a circle are supplementary. (p. 782)

    • Proof on p. 786, Exercise 33

Theorem 12-12

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. (p. 783)

• Proof on p. 786, Exercise 34

Theorem 12-13

The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs. (p. 790)

• Proof on p. 791

Theorem 12-14

The measure of an angle formed by two lines that intersect outside a circle is half the difference of the measures of the intercepted arcs. (p. 790)

• Proofs on p. 796, Exercises 35, 36

Theorem 12-15

For a given point and circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle.

(p. 793)

• Proofs on p. 793; p. 796, Exercises 37, 38

Theorem 12-16

An equation of a circle with center (h, k) and radius r is ( x − h ) 2 + ( y − k ) 2 = r 2 . open x minus . h , close squared , plus , open y minus . k , close squared , equals , r squared , . (p. 798)

• Proof on p. 799

Constructions

Construction 1

Congruent Segments

Construct a segment congruent to a given segment. (p. 43)

Construction 2

Congruent Angles

Construct an angle congruent to a given angle. (p. 44)

Construction 3

Perpendicular Bisector

Construct the perpendicular bisector of a segment. (p. 45)

Construction 4

Angle Bisector

Construct the bisector of an angle. (p. 45)

Construction 5

Parallel Through a Point Not on a Line

Construct the line parallel to a given line and through a given point that is not on the line. (p. 182)

Construction 6

Quadrilateral With Parallel Sides

Construct a quadrilateral with one pair of parallel sides of lengths a and b. (p. 183)

Construction 7

Perpendicular Through a Point on a Line

Construct the perpendicular to a given line at a given point on the line. (p. 184)

Construction 8

Perpendicular Through a Point Not on a Line

Construct the perpendicular to a given line through a given point not on the line. (p. 185)

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