Mathematics for IGCSE & O level - Circle Theorems (Section 3)
1
In a circle, what is the angle subtended at the center by a minor arc, if the angle subtended at the circumference by the same arc is 30 degrees?
Answer
(C)
60 degrees
2
If two chords of a circle intersect at right angles, what can we conclude about the arcs they intercept?
Answer
(B)
The arcs are complementary.
3
If two tangents are drawn to a circle from a point outside the circle and form an angle of 60 degrees, what type of triangle is formed by the tangents and the segment joining the center of the circle to the external point?
Answer
(A)
Equilateral
4
Consider a circle with center O. Chord AB is perpendicular to radius OC. What is the relationship between OC and AB?
Answer
(A)
OC bisects AB.
5
In a circle, how is the angle at the center related to the angle at the circumference subtended by the same arc?
Answer
(C)
The center angle is double the circumference angle.
6
In a cyclic quadrilateral ABCD, angle A is 80 degrees. What is the measure of angle C?
Answer
(C)
100 degrees
7
If two chords intersect inside a circle, how are the angles formed related to the intercepted arcs?
Answer
(A)
The angle is half the sum of the intercepted arcs.
8
What type of angle is formed between a tangent and a radius drawn to the point of tangency?
Answer
(C)
Right
9
What is the relationship between the angle formed by two tangents from an external point and the major arc intercepted by the tangents?
Answer
(A)
They are supplementary.
10
Which of the following theorems describes the relationship between a tangent to a circle and a chord drawn from the point of tangency?
Answer
(B)
Alternate segment theorem
11
Which of the following must be equal if they intercept the same arc?
Answer
(B)
Angles at the circumference
12
What is the measure of the angle between a tangent and a chord drawn from the point of tangency?
Answer
(C)
Equal to the angle in the alternate segment.
13
What do we know about the relationship between the lengths of tangents drawn from an external point to a circle?
Answer
(B)
They are always equal.
14
What is the measure of an angle inscribed in a semicircle?
