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Factor Warm – up Session 48 27 xx
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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
12