1. Geometry Lines That Intersect Circles
CONFIDENTIAL

2. Warm Up A Point is chosen randomly on .
Use the diagram to find the probability of each event.
1) The point is not on
2) The point is on
3) The point is or
4) The point is on
1) ¾ 2) ½ 3) 13/20 4) 1/40
CONFIDENTIAL

3. Lines That Intersect Circles
A Circle is the set of all points in a plane that are equidistant from a given point , called the center of the circle . A circle with center C is called circle C, or C.
The Interior of a circle is the set of all points inside the circle . The exterior of a circle is the set of all points outside the circle.
CONFIDENTIAL

4. Lines and Segments That Intersects circles
TERM
DIAGRAM
A Chord is a segment whose end points lie on a circle.
A Secant is a line that intersects a circle at two points.
A Tangent is a line in the same plane as a circle that intersects it at exactly one point.
The point where the tangent and a circle intersect is called the point of tangency.
CONFIDENTIAL

5. Identifying Lines and Segments That Intersect Circles
Identify each line or segment that intersect A.
chords: and
tangent: L
radii: and
secant:
diameter:
CONFIDENTIAL

6. Identify each line or segment that intersects P.
Now you try
Identify each line or segment that intersects P.
chord: QR
tangent: UV
radii: SP and PT
secant: ST
diameter: ST
CONFIDENTIAL

7. Remember that the terms radius and diameter may refer to line segments, or to the lengths of segments
CONFIDENTIAL

8. TERM
CONDITION
Two circles are congruent circles if and only if they have congruent radii.
Concentric circles are coplanar circles with the same center.
CONFIDENTIAL

9. Two coplanar circles that intersect at exactly one point are called tangent circles
CONFIDENTIAL

10. Identifying Tangents of a circles
Find the length of each radius . Identify the point of tangency and write the equation of the tangent line at this point. A B X Y -4 4 -2 2
CONFIDENTIAL

11. A B X Y -4 4 -2 2
CONFIDENTIAL

12. Find the length of each radius.
Now you try
Find the length of each radius.
Identify the point of tangency and write the equation of the tangent line at this point -4 4
Point of tangency: (2, -1)
equation of the tangent: y = -1
CONFIDENTIAL

13. A common tangent is a line that is tangent to two circles
CONFIDENTIAL

14. B A p q
CONFIDENTIAL

15. Tangent to a circle at a point
Construction
Tangent to a circle at a point 2) 1)
CONFIDENTIAL

16. 3) l
CONFIDENTIAL

17. The tangent line is perpendicular to the radius at the point of tangency. This fact is the basis for the following theorems .
CONFIDENTIAL

18. THEOREM
HYPOTHESIS
CONCLUSION 1) 2) B l A
CONFIDENTIAL

19. THEOREM
HYPOTHESIS
CONCLUSION 3)
CONFIDENTIAL

20. Using Properties of Tangents
CONFIDENTIAL

21. Now you try 1) R S T
X- 6.3
RS = 2.1
CONFIDENTIAL

22. Now you try 2) S T R
n+3
2n-1
RS = 7
CONFIDENTIAL

23. Now some problems for you to practice.
CONFIDENTIAL

24. Identify each line or segment that intersects each circle.
ASSESSMENT
Identify each line or segment that intersects each circle. 1) F D E m l 2) T Q S
CONFIDENTIAL

25. 3)
Find the length of each radius . Identify the point of tangency and write the equation of the tangent line at this point. X Y A B -4 4
Point of tangency: (-1, 4)
equation of the tangent: y = 4
CONFIDENTIAL

26. 4)
Find the length of each radius . Identify the point of tangency and write the equation of the tangent line at this point. X Y R S -4 4
length of radius OS = 2
Point of tangency: (2, 0)
equation of the tangent: y = 0
length of radius OR = 2
Point of tangency: (-1, 0)
equation of the tangent: y = 0
CONFIDENTIAL

27. The segments in each figure are tangent to the circle. Find length JK.5)
The segments in each figure are tangent to the circle. Find length JK. K C L J
4x-1
2x+9
JK = 7
CONFIDENTIAL

28. The segments in each figure are tangent to the circle. Find length ST.6)
The segments in each figure are tangent to the circle. Find length ST. T P U S
Y- 4 3 4 y
ST = 12
CONFIDENTIAL

29. Lines and Segments That Intersects circles
REVIEW
Lines and Segments That Intersects circles
TERM
DIAGRAM
A Chord is a segment whose end points lie on a circle.
A Secant is a line that intersects a circle at two points.
A Tangent is a line in the same plane as a circle that intersects it at exactly one point.
The point where the tangent and a circle intersect is called the point of tangency.
CONFIDENTIAL

30. Identifying Lines and Segments That Intersect Circles
Identify each line or segment that intersect A.
chords: and
tangent: L
radii: and
secant:
diameter:
CONFIDENTIAL

31. TERM
CONDITION
Two circles are congruent circles if and only if they have congruent radii.
Concentric circles are coplanar circles with the same center.
CONFIDENTIAL

32. Two coplanar circles that intersect at exactly one point are called tangent circles
CONFIDENTIAL

33. Identifying Tangents of a circles
Find the length of each radius . Identify the point of tangency and write the equation of the tangent line at this point. A B X Y -4 4 -2 2
CONFIDENTIAL

34. A B X Y -4 4 -2 2
CONFIDENTIAL

35. Find the length of each radius.
Now you try
Find the length of each radius.
Identify the point of tangency and write the equation of the tangent line at this point -4 4
CONFIDENTIAL

36. A common tangent is a line that is tangent to two circles
CONFIDENTIAL

37. B A p q
CONFIDENTIAL

38. THEOREM
HYPOTHESIS
CONCLUSION 1) 2) B l A
CONFIDENTIAL

39. THEOREM
HYPOTHESIS
CONCLUSION 3)
CONFIDENTIAL

40. Using Properties of Tangents
CONFIDENTIAL

41. You did a great job today!
CONFIDENTIAL