Q. If a circle has a diameter of 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?
A.
5.24 cm
B.
10.47 cm
C.
3.14 cm
D.
6.28 cm
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Solution
The length of an arc is given by L = (θ/360) * 2πr. Here, r = 5 cm, so L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. If a circle has a radius of 5 cm, what is the area of the circle?
A.
25π cm²
B.
10π cm²
C.
20π cm²
D.
15π cm²
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Solution
The area of a circle is given by the formula A = πr². Thus, A = π(5)² = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. If a circle has a radius of 7 cm, what is the area of the circle?
A.
154 cm²
B.
49 cm²
C.
44 cm²
D.
28 cm²
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Solution
The area of a circle is given by the formula A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
Correct Answer:
A
— 154 cm²
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Q. If a tangent from point P touches a circle at point T, what is the relationship between the radius OT and the tangent PT?
A.
OT is equal to PT
B.
OT is perpendicular to PT
C.
OT is parallel to PT
D.
OT is longer than PT
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Solution
The radius drawn to the point of tangency is perpendicular to the tangent line at that point.
Correct Answer:
B
— OT is perpendicular to PT
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Q. If a tangent from point P touches the circle at point T, which of the following statements is true?
A.
PT is perpendicular to the radius OT
B.
PT is parallel to the radius OT
C.
PT is equal to the radius OT
D.
PT bisects the angle OTP
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Solution
The tangent to a circle at any point is perpendicular to the radius drawn to the point of tangency.
Correct Answer:
A
— PT is perpendicular to the radius OT
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Q. If the diameter of a circle is 14 cm, what is the circumference of the circle?
A.
22 cm
B.
28 cm
C.
44 cm
D.
14 cm
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Solution
The circumference C of a circle is given by C = πd. Here, d = 14 cm, so C = π * 14 ≈ 43.98 cm, which rounds to 44 cm.
Correct Answer:
B
— 28 cm
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Q. If the radius of a circle is doubled, how does the area of the circle change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
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Solution
The area of a circle is given by A = πr². If the radius is doubled (r' = 2r), the new area A' = π(2r)² = 4πr², which is four times the original area.
Correct Answer:
D
— It quadruples
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Q. If two circles intersect at points A and B, and the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?
A.
It bisects AB
B.
It is equal to AB
C.
It is longer than AB
D.
It is shorter than AB
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Solution
The perpendicular from the center of a circle to a chord bisects the chord.
Correct Answer:
A
— It bisects AB
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Q. If two circles intersect at points A and B, which of the following statements is true regarding the angles formed?
A.
Angle AOB is equal to angle ACB
B.
Angle AOB is equal to angle APB
C.
Angle ACB is equal to angle APB
D.
Angle AOB is equal to angle APB + angle ACB
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Solution
The angles subtended by the same arc at the circumference are equal, hence angle ACB = angle APB.
Correct Answer:
C
— Angle ACB is equal to angle APB
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Q. If two triangles are similar, which of the following is true about their corresponding sides?
A.
They are equal
B.
They are proportional
C.
They are congruent
D.
They are perpendicular
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Solution
In similar triangles, the corresponding sides are proportional to each other.
Correct Answer:
B
— They are proportional
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Q. In a circle, if the diameter is 14 cm, what is the circumference of the circle?
A.
43.96 cm
B.
28 cm
C.
14 cm
D.
21.99 cm
Show solution
Solution
The circumference of a circle is given by C = πd. Thus, C = π(14) ≈ 43.96 cm.
Correct Answer:
A
— 43.96 cm
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Q. In a circle, if the radius is 5 cm, what is the length of an arc that subtends a central angle of 60 degrees?
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
The length of an arc is given by L = (θ/360) * 2πr. Thus, L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. In a circle, if the radius is doubled, what happens to the area of the circle?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
The area of a circle is given by A = πr². If the radius is doubled, the new area becomes π(2r)² = 4πr², which is four times the original area.
Correct Answer:
D
— It quadruples
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Q. In a circle, if two chords AB and CD intersect at point E, which of the following is true?
A.
AE * EB = CE * ED
B.
AE + EB = CE + ED
C.
AE - EB = CE - ED
D.
AE / EB = CE / ED
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Solution
According to the intersecting chords theorem, the products of the segments of the chords are equal, hence AE * EB = CE * ED.
Correct Answer:
A
— AE * EB = CE * ED
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Q. In triangle ABC, if angle A is 50 degrees and angle B is 70 degrees, what is the measure of angle C?
A.
60 degrees
B.
70 degrees
C.
80 degrees
D.
90 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 70) = 60 degrees.
Correct Answer:
C
— 80 degrees
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Q. What is the relationship between the angles subtended by the same arc at the center and on the circumference of a circle?
A.
They are equal
B.
The angle at the center is twice the angle at the circumference
C.
The angle at the circumference is twice the angle at the center
D.
They are complementary
Show solution
Solution
The angle subtended at the center of a circle is always twice the angle subtended at the circumference by the same arc.
Correct Answer:
B
— The angle at the center is twice the angle at the circumference
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