MathematicsCircle Geometry
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Circles and Arc Measurements Quiz

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#1

Which of the following is the formula for calculating the circumference of a circle?

C = 2πr
Explanation

Circumference equals twice pi times radius.

#2

If the radius of a circle is 5 units, what is the diameter?

10 units
Explanation

Diameter is twice the radius.

#3

What is the name of the line segment that passes through the center of a circle and has endpoints on the circle?

Radius
Explanation

Radius is the segment connecting the center to any point on the circle.

#4

If the diameter of a circle is 12 units, what is the circumference?

24π units
Explanation

Circumference equals pi times diameter.

#5

What is the measure of a central angle that subtends an arc of 45 degrees in a circle?

45 degrees
Explanation

Central angle equals arc measure.

#6

In a circle, if the radius is 8 units and the central angle is 60 degrees, what is the length of the intercepted arc?

8π units
Explanation

Arc length equals radius times central angle in radians.

#7

If the radius of a circle is tripled, how does it affect the area of the circle?

Area becomes nine times larger
Explanation

Area scales with the square of the radius.

#8

What is the measure of an inscribed angle that intercepts a semicircle in a circle?

90 degrees
Explanation

Inscribed angle intercepting a semicircle is a right angle.

#9

If the radius of a circle is 10 units, what is the area of the circle?

100π square units
Explanation

Area equals pi times radius squared.

#10

What is the relationship between the inscribed angle and the central angle subtended by the same arc in a circle?

The inscribed angle is half of the central angle
Explanation

Inscribed angle subtended by the same arc is half of the central angle.

#11

If the central angle of a circle is 120 degrees, what is the measure of the corresponding inscribed angle?

60 degrees
Explanation

Inscribed angle equals half of the central angle.

#12

In a circle with radius 6 units, what is the length of an arc subtended by a central angle of 120 degrees?

4π units
Explanation

Arc length equals radius times central angle in radians.

#13

What is the relationship between the radius and the tangent line at the point of tangency on a circle?

Perpendicular
Explanation

Radius and tangent line are perpendicular at the point of tangency.

#14

What is the measure of an angle formed by two radii in a circle with a central angle of 60 degrees?

30 degrees
Explanation

Angle formed by two radii is half of the central angle.

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