Circles

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.

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10.1 Notes

• Finding diameter given radius
• r6
• r1.7cm
• d12
• d3.4cm

12
10.1 Notes

• Finding diameter given radius
• r4ft
• d8ft
• r m
• d m

13
10.1 Notes

• Find diameter given radius
• 1.
• 2. r12m
• 3. r7ft

14
10.1 Notes

• Finding radius given diameter
• 1. 2.

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
• d9m
• r4.5m

18
10.1 Notes

• Find radius given diameter
• 1. AB30in
• PC?
• PC15in
• 2. d42ft
• r21ft
• 3. d10cm
• r5cm

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.

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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.