1. Section 10.1
Circles

2. 10.1 Notes
What is a CIRCLE?
A CIRCLE is the set of all points in a plane equidistant from a given point.

3. 10.1 Notes There are points ON, IN, and OUTSIDE the circle.
The points in the circle make up the INTERIOR of the circle.

4. 10.1 Notes There are points ON, IN, and OUTSIDE the circle.
The points outside the circle are EXTERIOR POINTS.

5. 10.1 Notes
A chord of a circle is a segment with both endpoints ON the circle.
is a chord.

6. 10.1 Notes
A diameter of a circle is a chord that passes through the center.
is a diameter.

7. 10.1 Notes
A radius of a circle is a segment with one endpoint at the center of the circle and the other endpoint on the circle.
and are radii.

8. 10.1 Notes
All radii are congruent since all points on the circle are equidistant from the center of the circle.

9. 10.1 Notes
Can you see a relationship between the radius and diameter of a circle?

10. 10.1 Notes A diameter of a circle is equal to two radii of the circle.
A radius of a circle is equal to half of a diameter of the circle.

11. 10.1 Notes
Finding diameter given radius:
r=6
r=1.7cm
d=12
d=3.4cm

12. 10.1 Notes
Finding diameter given radius:
r=4ft
d=8ft
r= m
d= m

13. 10.1 Notes
Find diameter given radius: 1.
2. r=12m
3. r=7ft

14. 10.1 Notes
Finding radius given diameter:

15. 10.1 Notes
Finding radius given diameter: 1.

16. 10.1 Notes
Finding radius given diameter: 2.

17. 10.1 Notes
Finding radius given diameter:
d= cm
r= cm
d=9m
r=4.5m

18. 10.1 Notes Find radius given diameter: 1. AB=30in PC=? PC=15in
2. d=42ft
r=21ft
3. d=10cm
r=5cm

19. 10.1 Notes
Tangent: a line which intersects a circle at exactly one point.
Point of tangency: the point where the tangent intersects the circle.

20. 10.1 Notes A common tangent is a line that is tangent to two circles.
A common tangent can either be a common external tangent or a common internal tangent.

21. 10.1 Notes
common external tangent

22. 10.1 Notes
common internal tangent

23. 10.1 Notes
common external tangent

24. 10.1 Notes
common internal tangent

25. 10.1 Notes
Secant: a line that intersects a circle at two points.

26. 10.1 Terms to know exterior points-points that lie outside a circle.
interior points-points that lie inside a circle.
chord- a segment whose endpoints are on the circle.
diameter-a chord that passes through the center of a circle.
radius-a segment with one endpoint at the center of the circle and the other endpoint on the circle.
tangent-a line which intersects a circle at exactly one point.
point of tangency-the point where the tangent intersects the circle.
common external tangent-a line that is tangent to two circles and DOES NOT intersect the segment connecting the two centers.
common internal tangent-a line tangent to two circles that DOES intersect the segment connecting the two centers.
secant-a line that intersects a circle at two points.