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?
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(A)
They are equal.
2
What is the relationship between a tangent and a radius of a circle at the point of tangency?
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(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?
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(A)
35 degrees
4
What can you say about the perpendicular from the centre of a circle to a chord?
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(C)
It bisects the chord and is perpendicular.
5
What is the sum of opposite angles in a cyclic quadrilateral?
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(B)
180 degrees
6
If two circles touch internally, how many common tangents can be drawn?
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(B)
2
7
If a line drawn from the center of a circle bisects a chord, what does that line do to the chord?
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(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?
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(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?
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(A)
They are equal.
10
What is the sum of the interior angles of a cyclic quadrilateral?
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(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?
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(C)
16 cm
12
The angle between a tangent and a radius drawn to the point of contact is always:
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(D)
90 degrees
13
Two equal chords AB and CD intersect at P inside the circle. What can you deduce about angles formed?
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C
D
14
In a cyclic quadrilateral ABCD, angle A is 80 degrees. What is the size of angle C?
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(B)
100 degrees
15
If a line from the center of a circle bisects a chord, what angle does it create with the chord?
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(D)
90 degrees
16
In the alternate segment theorem, what angle is equal to the angle between a tangent and a chord?
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(B)
The angle in the alternate segment
17
Which of the following is NOT a property of cyclic quadrilaterals?
پاسخ دهید
(D)
All sides are equal.
18
If two circles touch externally, how many common tangents can be drawn?
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(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?
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(C)
They are equal.
20
What is the relationship between two tangents drawn from an external point to a circle?
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(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?
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A
B
22
What is the angle between a tangent and a radius drawn to the point of contact?
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(C)
90 degrees
23
Which statement accurately reflects the angle properties of a semi-circle?
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(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?
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(B)
10 cm
25
What can you say about the chords in a circle that are equidistant from the center?
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(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?
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(B)
5 cm
27
What is always true about the angle between a tangent and a radius at the point of contact?
پاسخ دهید
(C)
90 degrees
28
What is the angle between a chord and a tangent at the point of contact equal to?
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(A)
Angle in the alternate segment
29
A tangent to a circle meets the radius at what angle?
پاسخ دهید
(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?
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(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?
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(C)
Alternate Segment Theorem.
32
Which geometric relationships are involved when determining the angles in a diagram with a circle and a tangent?
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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?
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(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?
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(C)
30 degrees
35
Which of the following statements are true regarding a tangent and a chord in a circle?
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A
C
36
If two chords intersect inside a circle, how are the angles formed related to the intercepted arcs?
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(A)
Each angle equals half the sum of the intercepted arcs.
37
What is the measure of an angle inscribed in a semicircle?
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(D)
90°
38
If two chords are equidistant from the center of a circle, which is true about their lengths?
پاسخ دهید
(A)
They are equal.
39
How many common tangents can be drawn to two circles that do not intersect?
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(D)
4
40
In a circle, the angle in a semi-circle is always:
پاسخ دهید
(D)
90 degrees
41
What does the perpendicular bisector of a chord pass through?
پاسخ دهید
(B)
The center of the circle
42
In a cyclic quadrilateral, what is the sum of any two opposite interior angles?
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(B)
180 degrees
43
In a cyclic quadrilateral, angle A is 110 degrees. What is the measure of its opposite angle C?
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(A)
70 degrees
44
What is the name of the theorem that states the angle in a semicircle is a right angle?
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(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?
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(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"?
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(D)
The alternate segment theorem.
47
What is true about opposite angles in a cyclic quadrilateral?
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(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?
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(C)
80°
49
What's the relationship between opposite angles in a cyclic quadrilateral?
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(B)
They're supplementary.
50
Which statements are accurate about the properties of circle theorems?
