1. 10.3 – Apply Properties of Chords

2. In the same circle, or in congruent circles, two ___________ arcs are congruent iff their corresponding __________ are congruent. A B C D then minor chords

3. If one chord is a _________________ _________ of another chord, then the first chord is the _________________. then perpendicular bisector diameter and is the diameter

4. If a ____________ of a circle is perpendicular to a chord, then the diameter ____________ the chord and its arc. then diameter bisects and the diameter

5. In the same circle, or in congruent circles, two chords are congruent iff they are _________________ from the _____________. then equidistantcenter and

6. 1. Find the given measure of the arc or chord. Explain your reasoning. =105° Congruent chords

7. 1. Find the given measure of the arc or chord. Explain your reasoning. = 360 4 Congruent chords = 90°

8. 1. Find the given measure of the arc or chord. Explain your reasoning. = 360 – 116 2 Congruent chords = 122°

9. 1. Find the given measure of the arc or chord. Explain your reasoning. = Congruent arcs 6

10. 1. Find the given measure of the arc or chord. Explain your reasoning. = Diameter bisects chord 22

11. 1. Find the given measure of the arc or chord. Explain your reasoning. = 119° 61° 119° Diameter bisects arc

12. =100° 50°

13. 360 – 85 – 65 2 = =105°

14. Find the value of x. 3x + 16 = 12x + 7 16 = 9x + 7 9 = 9x 1 = x

15. Find the value of x. 3x – 11 = x + 9 2x – 11 = 9 2x = 20 x = 10

16. YES or NO Reason: _______________________ it is perpendicular and bisects

17. YES or NO Reason: _______________________ it doesn’t bisect

18. 10.6 – Find Segment Lengths in Circles

19. If two chords intersect in the _______________ of a circle, then the ___________ of the lengths of the segments of one chord is equal to the product of the lengths of the segments o f the other chord. interior product

20. If two secant segments share the same endpoint ____________ a circle, then the ______________ of the lengths of one secant segment and its external segment equals the _____________ of the lengths of the other secant segment and its external segment. outsideproduct

21. If a secant segment and a tangent segment share an endpoint ____________ a circle, then the product of the lengths of the secant segment and its external segment equals the ___________ of the length of the tangent segment. outside square

22. Find the value of x. 3  x = 9  5 3x = 45 x = 15

23. Find the value of x. 3x = 5(5+10) 3x = 75 x = 25

24. Find the value of x. x 2 = 2(2+16) x 2 = 36 x = 6

25. Find the value of x. 6  x = 8  3 6x = 24 x = 4

26. Find the value of x. 2  x = 5  5 2x = 25 x = 12.5

27. Find the value of x. 5(x + 5) = 6(6+4) 5x + 25 = 60 x = 7 5x = 35

28. Find the value of x. x 2 = 3(3+24) x 2 = 81 x = 9

29. Find the value of x. 2x  3x = 3  18 6x 2 = 54 x 2 = 9 x = 3

30. Find the value of x. 31 2 = 20(x + 20) 961 = 20x + 400 561 = 20x 28.05 = x

31. 10.3 10.6 667-668 692-695 3-9, 12-14 3, 4, 6, 9, 13, 17 HW Problem 10.6 #6 8(x + 8) = 6(10+6) 8x + 64 = 96 x = 4 8x = 32