Q. If a circle has a circumference of 31.4 cm, what is the radius of the circle? (Use π = 3.14)
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A.
5 cm
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B.
10 cm
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C.
7 cm
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D.
15 cm
Solution
The circumference C of a circle is given by C = 2πr. Thus, 31.4 = 2 * 3.14 * r, which gives r = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If a tangent touches a circle at point A and a line from the center to point A is drawn, what is the angle between the tangent and the radius?
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A.
0 degrees
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B.
45 degrees
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C.
90 degrees
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D.
180 degrees
Solution
The tangent to a circle at any point is perpendicular to the radius drawn to the point of contact, hence the angle is 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. If the coordinates of the center of a circle are (3, 4) and the radius is 5, what is the equation of the circle?
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A.
(x-3)² + (y-4)² = 25
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B.
(x+3)² + (y+4)² = 25
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C.
(x-3)² + (y-4)² = 5
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D.
(x-3)² + (y-4)² = 20
Solution
The standard form of the equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x-3)² + (y-4)² = 25
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Q. If the diameter of a circle is 10 cm, what is the circumference?
-
A.
31.4 cm
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B.
25.0 cm
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C.
15.7 cm
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D.
20.0 cm
Solution
The circumference of a circle is given by C = πd. Here, C = π(10) ≈ 31.4 cm.
Correct Answer:
A
— 31.4 cm
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Q. If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 4 cm, what is the length of CE if ED = 2 cm?
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A.
6 cm
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B.
8 cm
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C.
4 cm
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D.
5 cm
Solution
Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 4 = CE * 2, which gives CE = 6 cm.
Correct Answer:
B
— 8 cm
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Q. If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 4 cm, what is the length of CE if ED = 6 cm?
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A.
2 cm
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B.
3 cm
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C.
4 cm
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D.
5 cm
Solution
Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 4 = CE * 6, which gives CE = 2 cm.
Correct Answer:
A
— 2 cm
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Q. If two chords in a circle are equal in length, what can be said about their corresponding arcs?
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A.
They are equal
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B.
One is longer
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C.
They are perpendicular
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D.
They intersect
Solution
Equal chords subtend equal arcs in a circle, hence their corresponding arcs are equal.
Correct Answer:
A
— They are equal
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Q. If two tangents are drawn from a point outside a circle to the circle, what is the relationship between the lengths of the tangents?
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A.
They are equal
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B.
One is longer
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C.
They are perpendicular
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D.
They are complementary
Solution
The lengths of the tangents drawn from an external point to a circle are always equal.
Correct Answer:
A
— They are equal
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Q. In a circle, if the central angle is 120 degrees, what fraction of the circle's area does the sector represent?
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A.
1/3
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B.
1/4
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C.
1/6
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D.
1/2
Solution
The area of the sector is proportional to the central angle. 120 degrees is 1/3 of 360 degrees, hence it represents 1/3 of the circle's area.
Correct Answer:
A
— 1/3
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Q. In a circle, if the central angle is 60 degrees, what fraction of the circle's area does the sector represent?
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A.
1/6
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B.
1/3
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C.
1/4
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D.
1/2
Solution
The area of a sector is proportional to the central angle. Since 60 degrees is 1/6 of 360 degrees, the sector represents 1/6 of the circle's area.
Correct Answer:
A
— 1/6
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Q. In a circle, if the diameter is 10 cm, what is the length of the radius?
-
A.
5 cm
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B.
10 cm
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C.
15 cm
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D.
20 cm
Solution
The radius is half of the diameter. Therefore, the radius is 10 cm / 2 = 5 cm.
Correct Answer:
A
— 5 cm
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Q. In a circle, if the radius is 5 cm, what is the area of the circle?
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A.
25π cm²
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B.
10π cm²
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C.
20π cm²
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D.
15π cm²
Solution
The area of a circle is given by the formula A = πr². Therefore, A = π(5)² = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?
-
A.
Scalene
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B.
Isosceles
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C.
Equilateral
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D.
Right
Solution
Triangle ABC is an isosceles right triangle because it has two equal sides and one right angle.
Correct Answer:
B
— Isosceles
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Q. What is the relationship between the angles in similar triangles?
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A.
They are equal
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B.
They are supplementary
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C.
They are complementary
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D.
They are congruent
Solution
In similar triangles, corresponding angles are equal.
Correct Answer:
A
— They are equal
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Q. What is the relationship between the angles subtended by the same arc at the center and at any point on the remaining part of the circle?
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A.
They are equal
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B.
The angle at the center is double
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C.
The angle at the center is half
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D.
They are supplementary
Solution
The angle subtended at the center is always double the angle subtended at any point on the remaining part of the circle.
Correct Answer:
B
— The angle at the center is double
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