1. Introduction to Circles
Section 11–1
Geometry PreAP, Revised ©2014
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11-1: Introduction to Circles

2. 11-1: Introduction to Circles
Definitions
Radius is a segment with one endpoint on the center of the circle and other on the circle itself
Diameter is a segment passing through he center with both endpoints on the circle
Chord is a segment with both endpoints on the circle
Secant is a line or ray that intersects a circle with two points
Tangent line segment or ray that intersects in exactly one point
Points of tangency is where the point where the tangent touches the circle
Arc is part of the circle on the outside
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11-1: Introduction to Circles

3. 11-1: Introduction to Circles
Example 1
Identify each line or segment that intersects Circle P.
Chords:
Secant:
Tangent:
Diameter:
Radii:
QR and ST ST UV ST
PQ, PT, and PS
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11-1: Introduction to Circles

4. 11-1: Introduction to Circles
Your Turn
Identify each line or segment that intersects Circle Q.
Chords:
Secant:
Tangent:
Diameter:
Radii:
VT and WR VT S WR
QW, QR
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11-1: Introduction to Circles

5. 11-1: Introduction to Circles
Pairs of Circles
Common Tangent is a line, ray, or segment that is tangent to two coplanar circles
Concentric Circles are coplanar circles if they have the same center
Tangent Circles are two coplanar circles that intersect at exactly one point
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11-1: Introduction to Circles

6. 11-1: Introduction to Circles
Common Tangents
Common Internal Tangent: Intersect the segment that joins the centers of the circles
Common External Tangent: Does not intersect the segment that joins the centers of the circles
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11-1: Introduction to Circles

7. Theorem 1
If a line is tangent to a circle, then it is perpendicular to the radius. B m
m is perpendicular to AB A

8. Theorem 2
If two segments are tangent to a circle from the same external point, then the segments are congruent.

9. 11-1: Introduction to Circles
Example 2
RS and RT are tangent to Q. Find RS.
RS = RT
x = 4x – 25.2
–3x = –25.2
x = 8.4
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11-1: Introduction to Circles

10. 11-1: Introduction to Circles
Your Turn
FE and FG are tangent to Circle F. Find FG.
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11. 11-1: Introduction to Circles
Example 3
B is a point of tangency. Find the radius r of Circle C.
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12. 11-1: Introduction to Circles
Your Turn
Point 𝑂 is a point of tangency. Find the radius of ⊙𝐶
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11-1: Introduction to Circles

13. 11-1: Introduction to Circles
Example 4
The area of circle H is 100π and HF = 26cm. What is the perimeter of quadrilateral EFGH?
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11-1: Introduction to Circles

14. 11-1: Introduction to Circles
Example 5
Early in its flight, the Apollo 11 spacecraft orbited Earth at an altitude of 120 miles. What was the distance from the spacecraft to Earth’s horizon if the radius of the Earth is 4000 miles?
EC = CD + ED
= = 4120 mi
EC2 = EH² + CH2
41202 = EH
974,400 = EH2
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11-1: Introduction to Circles

15. 11-1: Introduction to Circles
Your Turn
GPS satellites orbit about 11,000 miles above Earth. The mean radius of Earth is about 3959 miles. Because GPS signals cannot travel through Earth, a satellite can transmit signals only as far as points A and C from point B, as shown. Find BA.
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11-1: Introduction to Circles

16. 11-1: Introduction to Circles
Assignment
Page , 12, 15-27, all
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11-1: Introduction to Circles