Date:

Sec 10-1

Concept: Tangents to Circles

Objective: Given a circle, identify parts and properties as measured by a s.g.

Circle Activity – Draw a diagram illustrating the words listed below. Identify each word on the illustration. LOOK IN CH 10

Circle

Center

Radius

Diameter

Chord

Secant

Tangent

Tangent Circles

Concentric

Common Tangent

Interior of a circle

Exterior of a circle

Point of Tangency

Minor Arc

Major Arc

Inscribed Angle

Central Angle

Example: The diagram shows the layout of the streets on Mexcaltitlan Island.

1. Name 2 secants

2. Name two chords

3. Is the diameter of the circle greater than HC?

4. If ΔLJK were drawn, one of its sides would be tangent to the circle. Which side is it?

Tangent Circles

2 points of intersection

1 point of intersection

No points of intersection

Draw internal/external tangents

Thm 10-1: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Pl

Q

QP l

If l is tangent to circle Q at P, then

Example: If BC is tangent to circle A, find the radius of the circle.

Use the pyth. Thm.

r2+242 = (r+16)2

r2+576 = (r+16)(r+16)

r2+576 = r2+16r+16r+256

r2+576 = r2+32r+256576 = 32r + 256

-256 -256

320 = 32r

32 32

10 = r

A16

24

rr

B C

Example: A green on a golf course is in the shape of a circle. A golf ball is 8 feet from the edge of the green and 28 feet from a point of tangency on the green, as shown at the right. Assume that the green is flat.

1. What is the radius of the green

2. How far is the golf ball from the cup at the center?

Thm 10-2: in a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle

Pl

Q If l QP at P, then l is tangent to circle Q

Example: Is CE tangent to circle D?

43

45D

EC

11

Use the Pyth. Thm:

112+432 = 452

121+1849 = 2025

1970 ≠ 2025

No, it’s not tangent

Thm: If 2 segments from the same exterior point are tangent to a circle, then they are congruent.

R

T

S

P

If SR and TS are tangent to circle P, then SR TS

Example: AB and DA are tangent to circle C. Find x.

X2 – 4 = 21

+ 4 +4

X2 = 25

X=5

B

D

C

AX2 - 4

21

Statements Reasons

1.

2. PQTQ; QSQR

3. PQ=TQ;

QS=QR

4. PQ+QS = TQ+QR

5.

6.

1.

2.

3.

4.

5. Seg. Addition Post.

6.

Today’s Work

In Class:

HW:

Center

Circle: 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 P is called “circle P” or P

Radius

Diameter

Chord

Tangent

Secant