The document contains various questions and answers related to circles and geometry. It covers definitions of circle properties, calculations involving distances, angles, and areas, as well as the identification and properties of different geometrical figures. Additionally, it includes specific problems related to inscribed angles, secants, tangents, and coordinates of points.

1. Circles
Selected questions:

2. Circles
A closed plane whose
every point is equidistant
from a point within the
curve.
Answer: circle

3. Circles
The given point described
in the definition of the
circle.
Answer: center

4. Circles
The length around a circle.
Answer: circumference

5. Circles
A chord passing through
the center of the circle.
Answer: diameter

6. Circles
A segment whose
endpoints are points on
the circle.
Answer: chord

7. Circles
A line which intersects the
circle at exactly one point.
Answer: tangent line

8. Circles
A line which intersects the
circle at two points.
Answer: secant line

9. Circles
The set of all points whose
distance from the center is
less than the radius.
Answer: interior of the circle

10. Circles
The set of all points/
whose distance from the
center is greater than the
radius.
Answer: exterior of the circle

11. Circles
It is an angle in the circle
whose vertex is the center
of the circle.
Answer: central angle

12. Circles
An arc with a measure of
180 is a
Answer: semicircle

13. Circles
An inscribed angle of a
circle measures 45. What
is the measure of its
intercepted arc?
Answer: 90

14. Circles
Which of the following
ordered pairs is a point of
the circle with equation
x2 + y2 = 45?
a. ( -5,5) b. (3,-6)
Answer: b. ( 3, -6 )

15. Circles
The measure of the central
angle of a regular nonagon
is.
Answer: 40

16. Circles
The measure of a central
angle of a circle is equal to
the measure of its
intercepted arc.
Answer: The Central Angle-Intercepted Arc Postulate

17. Circles
The measure of an
inscribed angle is one-half
the measure of its
intercepted arc.
Answer: The Inscribed Angle Theorem

18. Circles
Two or more angles
inscribed in the same arc
are congruent.
Answer: The inscribed Angles in the same Arc Theorem

19. Circles
What is the distance
between the points (-2, 5)
and (4, -3)?
Answer: 10

20. Circles
What is the distance
between the points (3, -7)
and (6, 2)?
Answer:

21. Circles
(-3, 2) and (12, 10) are
points on opposite ends of
the diameter of a
circle. What is the radius
of the circle?
Answer: 8.5

22. Circles
The distance between the
points (-2, y) and (3, -7)
is 13 units. What are the
possible values for y?
Answer: y = -19 or 5

23. Circles
The coordinates of the
right-angled triangle ABC
are: A = (1,2), B = (3,6)
and C = (7,4). What is the
length of the hypotenuse
of the triangle?
Answer:

24. Circles
What is the midpoint of
the straight line segment
joining the points (-2, 5)
and (6, -1)?
Answer: (2, 2)

25. Circles
What is the midpoint of AB?
Answer:

26. Circles
What is the midpoint of
the straight line segment
joining the points (3, -6)
and (-4, -3)?
Answer:

27. Circles
What is the midpoint of
the straight line segment
joining the points (-2, 9)
and (3, -2)?
Answer:

28. Circles
What is the midpoint of
BC?
Answer:

29. Circles
Find the area of a circle
whose circumference is
4𝜋
3
?
Answer: 4𝜋
9

30. Circles
QP is tangent to circle O at
P. If 𝑚∠𝑃𝑂𝑄 = 73, what is
𝑚∠𝑄 ?
Answer: 17
O
P
Q

31. Circles
PS and PQ are secant and
tangent circle A. if arc
RQ is 52, what is 𝑚∠𝑃 ?
Answer: 26
S
R
A
Q
P

32. Circles
Answer: 85
C
A
B
D
E
Given circle E with secants AB
and CD if arc AC = 53 and arc
BD = 117, find 𝑚∠CEA ?

33. Circles
Answer: 26
P
S
R
Q
O
A
Given circle A with secants OQ and
OP if arc RS = 32 and arc QP=84,
find 𝑚∠𝑂 ?

34. Circles
Given 𝐴𝐵 ⊥ 𝐶𝐷 𝑎𝑡 𝐹, CD is
10cm long. How far is CD
from the center if the
length of the radius is 13
cm.
Answer: 12
F AB
C
D

35. Circles
Find the circumference of a
circle whose radius is
3
𝜋
𝑖𝑛 .
Answer: 6

36. Circles
The radius of a circle is 20.
Find the length of the arc
whose measure is 45o.
Answer: 5π

37. Circles
What is the center of a
circle with equation of
x2 +(y+7)2=25 ?
Answer: (0, -7)

38. Circles
What is the equation of
the circle whose center is
( -4, -3 ) and passing
through the origin ?
Answer: (x + 4)2 +(y + 3)2 = 25

39. Circles
Find the perimeter of a
triangle whose vertices are
at the given points
A(0,-4), B(3,0), C(0,0).
Answer: 12 units

40. Circles
Find the area of a triangle
whose vertices are at the
given points
A(0,-4), B(3,0), C(0,0).
Answer: 6 units

41. Circles
Draw a triangle with
vertices A(0,-4), B(3,0),
C(0,0). What kind of
triangle it is?
Answer: right triangle

42. Circles
If A is a the midpoint MN ,
determine the coordinates
of A if the coordinates of
the endpoints are M(-4,-3)
and N(4,3).
Answer: (0,0)

43. End
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