2.2 The Circle power point presentation

Power point

1. B C D P E A F G H J I Name the following: Circle Center Radius Chords Diameter Secant Tangent

2. M S A H If a radius is perpendicular to a chord, then it bisects the chord. Theorem 97 Given: Circle M with radius at T   T Conclusion: bisects   2(x – 3) x + 8

3. Quiz 2.1

4. O R A B at C, AC = 4x + 10, and BC = 7x – 5. Find AC, BC, and AB.   Quiz 2.1 C

5. O R A B AC = BC 4x + 10 = 7x – 5. -3x = -15 x = 5 Quiz 2.1 C

6. O R A B AC = 4(5) + 10 = 20 + 10 = 30 Quiz 2.1 C

7. O R A B BC = 7(5) – 5. = 35 – 5 = 30 Quiz 2.1 C

8. O R A B AB = AC + BC = 30 + 30 = 60 Quiz 2.1 C

9. If a radius is perpendicular to a chord, then it bisects the chord. Theorem 97 Theorem 98 If a radius bisects the chord (that is not a diameter), then it is perpendicular to a chord

10. O P A B Q Theorem 99 The perpendicular bisector of a chord passes through the center of the circle.

11. O P A B 5 cm 5 cm OA = PB = 5 cm Congruent Circles Congruent circles are circles that have congruent radii.

12. O C Concentric Circles Concentric circles are coplanar circles having the same center. B A

13. Draw a circle. Draw two chords equidistant from the center. Carefully measure the lengths of the two chords. What do you notice?

14. O D A B If chords of a circle (or of congruent circles) are equidistant from the center(s), then the chords are congruent. Theorem 100 E F C Given: Circle O, OC = OF Conclusion:  

15. O D A B If chords of a circle (or of congruent circles) are congruent, then they are equidistant from the center of the circle. Theorem 101 E F C Given: Circle O,   Conclusion: OC = OF

16. O B C D EO = OF = , and CD = . Find FD and radius of circle O.   A E F Given: Circle O,   Conclusion: OC = OF Example 2

17. O B C D TRUE or FALSE. If OE = OF, then   A E F Mental Math

18. O B C D TRUE or FALSE. If OE = OF, then   A E F Mental Math

19. O B C D TRUE or FALSE. If , then AB = 2AE   A E F Mental Math

20. O B C D TRUE or FALSE. If , then OE = OF   A E F Mental Math

21. Solve written Math (A, 8 and 9) on page 209. Seatwork 2.2

22. Solve written Math (A, 10 and 11 on page 209. Homework 2.1

23. A circle is the set of all points that are of the same distance from a given point in a plane. The given point is called the center of the circle. The segment from the center to any point on the circle is called the radius . A segment whose endpoints both lie on the circle is called the chord . A chord that passes through the center of the circle is called diameter . A secant is a line that intersects the circle in two points . A tangent is a line that intersects the circle in exactly one point.