EOC Practice
EOC Practice
Question of the Day
Intersections of
Circles and
Tangent Segments
Two circles can intersect:
in
two
points
one
point
or
no
points
No
points of intersection,
but
different
centers
Concentric Circles
Have
no
points
of intersection,
but the
same
center
Same center
but different
radii
One
point of intersection
are called Tangent Circles
Internally
Tangent
Externally
Tangent
TWO
points of intersection
Common
Internal
Tangents
Common
External
Tangents
leg
2
+ leg
2
= hyp
2
x = 15
9
2
+ 12
2
= x
2
leg
2
+ leg
2
= hyp
2
RQ = 16
12
2
+ (RQ)
2
= (8+12)
2
12
2
+ (RQ)
2
= 20
2
No
leg
2
+ leg
2
= hyp
2
?
16
2
+ 24
2
= 32
2
?
r
2
+ 24
2
= (r + 16)
2
r = 10
r
2
+ 576
= r
2
+ 32r + 256
320
= 32r
5. 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
If two segments from
the same exterior
point are tangent to
a circle, then they
are congruent.
R
S
T
R
S
T
A
C
B
A
C
E
B
D
P
3
4
T
S
Q
P
N
R
4
8
8
10
In geometry, understanding the relationships between circles and tangent segments is crucial. Explore how circles can intersect in different ways and discover the properties of concentric circles, tangent circles, and more.
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Presentation Transcript
EOC Practice Question of the Day
Intersections of Circles and Tangent Segments
Two circles can intersect: in two points one point or no points
No points of intersection, but different centers
Concentric Circles Have no points of intersection, but the same center Same center but different radii
One point of intersection are called Tangent Circles Externally Tangent Internally Tangent
1. Find the value of x. A 12 B 9 x leg2 + leg2 = hyp2 92 + 122 = x2 x = 15
2. Find the length of RQ. leg2 + leg2 = hyp2 122 + (RQ)2 = (8+12)2 P 12 122 + (RQ)2 = 202 8 R Q RQ = 16
3. Is CB tangent to the circle? leg2 + leg2 = hyp2? 162 + 242 = 322 ? A 32 C 16 24 B No
4. Find the radius. r2 + 242 = (r + 16)2 r2 + 576= r2 + 32r + 256 320= 32r 16 A C r = 10 24 B
5. 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? x = 60 ft. b) How far is your ball from the cup at the center? x = 68 ft.
RS TS S If two segments from the same exterior point are tangent to a circle, then they are congruent. R T Party hat problems!
6. Find the value of x. 3 x + 4 R S 16 3 x + 4 x = 16 4 = T
7. Find the value of x. 2 x + 2 R S 2 x + x = or x 2 11 9 3 = 11 2 T x 3 = =
8. Find the value of x. C 14x A 2 x 14 15 ) 1 + 15 B 2 x x ( x 15 14 15 x = x 2 x 0 0 = = = 15 x )(
9. Find the value of x. B 3 3 x A C 4 P D 4 E x = 7
10. Find the length of NP. NP = 18 N 8 8 12 T S 10 4 P R 4 10 Q
