2. Learning About Circles

3. Circle n An infinite set of coplanar points that are an equal distance from a given point. O M M

4. Center n The point at the middle of the circle. n point M M

5. Radius n A segment whose endpoints are the center of a circle and a point on the circle. n A MA M

6. Chord n A segment whose endpoints are points on a circle. n A n B AB M

7. Diameter n A chord that contains the center of a circle. n A n B n n T AT M In O M

8. Circumference n The distance around a circle. C = 2  r M

9. Area n Number of square units contained in the interior of a circle. n n n n A =  r 2

10. Central Angle n An angle whose vertex is the center of a circle. n n A n B n n / AMB M

11. Arc n A continuous portion of the circle.

12. Minor Arc n An arc that is less than half of a circle. 0 O < x O < 180 O n A n B n n C AB (

13. Semicircle Semicircle n An arc whose measure is 180 O, exactly half of a circle. n n A B n T M AT when AT contains M M (

14. Major Arc Major Arc n An arc whose measure is more than half and less than one whole circle. 180 O < x O < 360 O n A n B n n C BAC (

15. Adjacent Arcs n Two arcs that share exactly one point. n A n B n C CA & AB ( (

16. Congruent Circles n Circles that have congruent radii. (circumferences, areas…)

17. Congruent Arcs n Two arcs in the same circle or congruent circles that have the same measure. n n B n C CA  AB ( ( A

18. Interior of the Circle n An infinite set of points inside the circle including the center. n n H I M K O M

19. Exterior of the Circle n All coplanar points that are outside a circle. R S T V P

20. Secant n A line that intersects a circle in exactly two points. n A n B n n C AB

21. Tangent n A coplanar line that intersects a circle in exactly one point. n A n B n D n C DB

22. Point of Tangency n The point in which a tangent intersects the circle. n A n B n D n C point B

23. Tangent Segments n Segment whose endpoints are a point on the tangent line and the point of tangency. n A n B n E n C BE

24. Common Tangent A line or segment that is tangent to two coplanar circles.

25. 4 Common Tangents

26. 3 Common Tangents

27. 2 Common Tangents

28. 1 Common Tangent

29. 0 Common Tangent

30. Arc of the Chord n An arc that has the same endpoints as a chord. n A n B n n C CA & CA (

31. Inscribed Angle n An angle whose vertex is on the circle and whose sides are chords of the circle. n A n B n C / ABC

32. Intercepted Arc n An arc whose endpoints are the non-vertex points of an inscribed angle that intersect the circle. n A n B n n C AC (

33. Inscribed Polygon n A polygon where each of its vertices lies on a circle. n A n B n C n D quadrilateral ABDC

34. Circumscribed Polygon n A polygon with ALL sides tangent to a circle. n A n B n D n n F C pentagon ADCFB

35. Secant Segment n A segment on a secant from the exterior of a circle to a point on the circle so that it contains the chord. n B n C n A n AB

36. External Secant Segment n Part of secant segment that is in the exterior of the circle. n A n B n D n C BD

37. Arc Length n The length of the arc; part of the circumference proportional to the central angle. n A n B n m AB = x 360 O Circ. (

38. Arc Bisector n Any line, ray or segment that contains the midpoint of an arc. n A n B n C CA  AB ( (

39. Concentric Circles n Coplanar circles that have the same center.

40. Similar Circles n All circles are similar.

41. Space The set of all points. n

42. Sphere n An infinite set of points in space that are an equal distance from a given point.