252.5

158.4

107.3

12.2

145.1

2

2

2

2

2

xx

xx

xx

xx

xx

Factor Warm – up Session 48 27 xx

43 xx

25 xx

35 xx

212 xx

EOCT Review

Homework Review

CCGPS Geometry

UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MMC9-12.G.C.1-5,G.GMD.1-3

Today’s Question:What other angle relationships do we know for circles?Standard: MMC9-12.G.C.2

TANGENT: a LINE that intersects the circle exactly ONE

time

Point of Tangenc

y

Two circles can intersect…

•in two points•one point•or no points

No points of intersection (different center)

No points of intersection (same center)

Same center but different radii

1 point of intersection(Tangent Circles)

Internally Tangent

Externally Tangent

2 points of intersection

If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Point of Tangenc

y

More Pythagorean Theorem type problems! Yeah!!

a2 + b2 = c2

x = 15

92 + 122 = x2

a2 + b2 = c2

RQ = 16

122 + (QR)2 = (8+12)2

122 + (QR)2 = 202

No

a2 + b2 = c2 ?

r2 + 242 = (r + 16)2

r = 10

r2 + 576 = r2 + 32r + 256320 = 32r

A green on a golf course is in the shape of a circle. Your golf ball is 8 feet from the edge of the green and 32 feet from a point of tangency on the green.

a)What is the radius?

b) How far is your ball from the cup at the center?

x = 60 ft.

x = 68 ft.

R

S

T

TSRS If two segments from

the same exterior point are tangent to a circle, then they are

congruent.

Party hat problems!

R

S

T

3 4x

16 3 4 16x

4x

R

S

T

22 x

11 1122 x92 x

3 3 xorx

A

C

B152 x

x14

15x

AC

E

3

4

7X

B

D

X

P

TS

Q10 4

18NP

P

N

R

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