Mathematics for IGCSE & O level - Circle Theorems (Section 1)
1
In a circle, if two chords are equidistant from the center, what can be said about the length of those chords?
Answer
(A)
They are equal.
2
What is the relationship between a tangent and a radius of a circle at the point of tangency?
Answer
(B)
They are perpendicular.
3
If an arc subtends an angle of 70 degrees at the center, what angle does it subtend at a point on the major arc?
Answer
(A)
35 degrees
4
What can you say about the perpendicular from the centre of a circle to a chord?
Answer
(C)
It bisects the chord and is perpendicular.
5
What is the sum of opposite angles in a cyclic quadrilateral?
Answer
(B)
180 degrees
6
If two circles touch internally, how many common tangents can be drawn?
Answer
(B)
2
7
If a line drawn from the center of a circle bisects a chord, what does that line do to the chord?
Answer
(C)
It's perpendicular to the chord.
8
If a tangent and a secant are drawn from an external point to a circle, how are they related?
Answer
(D)
They intersect the circle at different points.
9
If two chords of a circle are equal, what can you deduce about their distances from the center?
Answer
(A)
They are equal.
10
What is the sum of the interior angles of a cyclic quadrilateral?
Answer
(C)
360 degrees
11
What is the length of a chord that is 8 cm from the center of a circle with a radius of 10 cm?
Answer
(C)
16 cm
12
The angle between a tangent and a radius drawn to the point of contact is always:
Answer
(D)
90 degrees
13
Two equal chords AB and CD intersect at P inside the circle. What can you deduce about angles formed?
Answer
C
D
14
In a cyclic quadrilateral ABCD, angle A is 80 degrees. What is the size of angle C?
Answer
(B)
100 degrees
15
If a line from the center of a circle bisects a chord, what angle does it create with the chord?
Answer
(D)
90 degrees
16
In the alternate segment theorem, what angle is equal to the angle between a tangent and a chord?
Answer
(B)
The angle in the alternate segment
17
Which of the following is NOT a property of cyclic quadrilaterals?
Answer
(D)
All sides are equal.
18
If two circles touch externally, how many common tangents can be drawn?
Answer
(C)
3
19
What is the relationship between the angle formed by a tangent and a chord at the point of contact and the angle in the alternate segment?
Answer
(C)
They are equal.
20
What is the relationship between two tangents drawn from an external point to a circle?
Answer
(B)
They have the same length.
21
Two equal chords AB and CD of a circle intersect at a point P inside the circle. Which is correct?
Answer
A
B
22
What is the angle between a tangent and a radius drawn to the point of contact?
Answer
(C)
90 degrees
23
Which statement accurately reflects the angle properties of a semi-circle?
Answer
(B)
The angle is always 90 degrees.
24
If a chord is 10 cm long and is 12 cm from the center of the circle, what is the radius of the circle?
Answer
(B)
10 cm
25
What can you say about the chords in a circle that are equidistant from the center?
Answer
(B)
They are equal in length.
26
If a chord of length 8 cm is 3 cm away from the center of a circle, what is the radius of the circle?
Answer
(B)
5 cm
27
What is always true about the angle between a tangent and a radius at the point of contact?
Answer
(C)
90 degrees
28
What is the angle between a chord and a tangent at the point of contact equal to?
Answer
(A)
Angle in the alternate segment
29
A tangent to a circle meets the radius at what angle?
Answer
(D)
90 degrees
30
Which theorem is most useful in determining the angles formed by a chord and a tangent at the point of contact?
Answer
(B)
Alternate Segment Theorem
31
What theorem relates the angle formed by a tangent and a chord with an angle in the alternate segment of the circle?
Answer
(C)
Alternate Segment Theorem.
32
Which geometric relationships are involved when determining the angles in a diagram with a circle and a tangent?
Answer
A
B
33
If a chord of a circle subtends an angle of 120 degrees at the center, what is the angle subtended by the same chord at a point on the major arc?
Answer
(B)
60°
34
If a chord subtends an angle of 60 degrees at the center of a circle, what is the angle it subtends at the circumference?
Answer
(C)
30 degrees
35
Which of the following statements are true regarding a tangent and a chord in a circle?
Answer
A
C
36
If two chords intersect inside a circle, how are the angles formed related to the intercepted arcs?
Answer
(A)
Each angle equals half the sum of the intercepted arcs.
37
What is the measure of an angle inscribed in a semicircle?
Answer
(D)
90°
38
If two chords are equidistant from the center of a circle, which is true about their lengths?
Answer
(A)
They are equal.
39
How many common tangents can be drawn to two circles that do not intersect?
Answer
(D)
4
40
In a circle, the angle in a semi-circle is always:
Answer
(D)
90 degrees
41
What does the perpendicular bisector of a chord pass through?
Answer
(B)
The center of the circle
42
In a cyclic quadrilateral, what is the sum of any two opposite interior angles?
Answer
(B)
180 degrees
43
In a cyclic quadrilateral, angle A is 110 degrees. What is the measure of its opposite angle C?
Answer
(A)
70 degrees
44
What is the name of the theorem that states the angle in a semicircle is a right angle?
Answer
(C)
Angle in a Semicircle Theorem
45
If a line from the center of a circle meets a chord at right angles, what does it do to the chord?
Answer
(A)
It bisects the chord.
46
Which of the following theorems is illustrated by the statement: "The angle between a tangent and a chord equals one angle made by their chord in the alternate segment of the circle"?
Answer
(D)
The alternate segment theorem.
47
What is true about opposite angles in a cyclic quadrilateral?
Answer
(B)
They are supplementary.
48
If a chord makes an angle of 40° at the circumference of a circle, what angle does it make at the center?
Answer
(C)
80°
49
What's the relationship between opposite angles in a cyclic quadrilateral?
Answer
(B)
They're supplementary.
50
Which statements are accurate about the properties of circle theorems?
