Presentation is loading. Please wait.

Presentation is loading. Please wait.

CHAPTER 9 Tangents, Arcs, and Chords. SECTION 9-1 Basic Terms.

Similar presentations


Presentation on theme: "CHAPTER 9 Tangents, Arcs, and Chords. SECTION 9-1 Basic Terms."— Presentation transcript:

1 CHAPTER 9 Tangents, Arcs, and Chords

2 SECTION 9-1 Basic Terms

3 is the set of points in a plane at a given distance from a given point in that plane. The given point is the CENTER of the circle and the given distance is the RADIUS. CIRCLE

4 is a segment whose endpoints lie on a circle. CHORD

5 is a line that contains a chord. SECANT

6 is a chord that contains the center of a circle. DIAMETER

7 is a line in the plane of a circle that intersects the circle in exactly one point, called the point of tangency. TANGENT

8 is the set of all points in space at a distance r (radius) from point O (center) SPHERE

9 Are circles that have congruent radii CONGRUENT CIRCLES

10 Are spheres that have congruent radii CONGRUENT SPHERES

11 Are circles that lie in the same plane and have the same center CONCENTRIC CIRCLES

12 Are spheres that have the same center. CONCENTRIC SPHERES

13 Occurs when each vertex of a polygon lies on the circle and the circle is CIRCUMSCRIBED about the POLYGON INSCRIBED in a CIRCLE

14 SECTION 9-2 Tangents

15 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. THEOREM 9 -1

16 Tangents to a circle from a point are congruent Corollary

17 If a line in the plane of a circle is perpendicular to the radius at its outer endpoint, then the line is tangent to the circle. THEOREM 9 -2

18 Occurs when each side of a polygon is tangent to a circle and the circle is INSCRIBED in the POLYGON CIRCUMSCRIBED about the CIRCLE

19 a line that is tangent to each of two coplanar circles COMMON TANGENT

20 Intersects the segment joining the centers of the circles. COMMON Internal TANGENT

21 Does not intersect the segment joining the centers of the circles. COMMON External TANGENT

22 are coplanar circles that are tangent to the same line at the same point TANGENT CIRCLES

23 SECTION 9-3 Arcs and Central Angles

24 is an angle with its vertex at the center of the circle. CENTRAL ANGLE

25 is an unbroken part of a circle. ARC

26 is the arc formed by two points on a circle * The measure of a minor arc is the measure of its central angle MINOR ARC

27 is the remaining arc formed by the remaining points on the circle * The measure is 360° minus the minor arc MAJOR ARC

28 is an arc formed from the endpoints of a circle’s diameter * The measure is 180° SEMICIRCLE

29 Arcs that have exactly one point in common. ADJACENT ARCS

30 Arcs in the same circle or in congruent circles that have equal measure. CONGRUENT ARCS

31 The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs POSTULATE 16

32 In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent. THEOREM 9-3

33 SECTION 9-4 Arcs and Chords

34 In the same circle or in congruent circles: 1. Congruent arcs have congruent chords 2. Congruent chords have congruent arcs THEOREM 9-4

35 A diameter that is perpendicular to a chord bisects the chord and its arc THEOREM 9-5

36 In the same circle or in congruent circles: 1. Chords equally distant from the center (or centers) are congruent 2. Congruent chords are equally distant from the center (or centers) THEOREM 9-6

37 SECTION 9-5 Inscribed Angles

38 Is an angle whose vertex is on a circle and whose sides contain chords of the circle. INSCRIBED ANGLE

39 Is the intersection of the sides of an inscribed angle and the circle INTERCEPTED ARC

40 The measure of an inscribed angle is equal to half the measure of its intercepted arc THEOREM 9-7

41 If two inscribed angles intercept the same arc, then the angles are congruent COROLLARY 1

42 An angle inscribed in a semicircle is a right angle. COROLLARY 2

43 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary COROLLARY 3

44 The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. THEOREM 9-8

45 SECTION 9-6 Other Angles

46 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. THEOREM 9-9

47 the measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs THEOREM 9-10

48 SECTION 9-7 Circles and Lengths of Segments

49 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 THEOREM 9-11

50 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. THEOREM 9-12

51 When a secant 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 THEOREM 9-13

52 END


Download ppt "CHAPTER 9 Tangents, Arcs, and Chords. SECTION 9-1 Basic Terms."

Similar presentations


Ads by Google