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Circles and Angles in Geometry Quiz

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#1

In a circle, what is the measure of a central angle that intercepts an arc with a measure of 90 degrees?

90 degrees
Explanation

Central angle equals the intercepted arc's measure.

#2

In a circle with a diameter of 10 units, what is the length of the radius?

5 units
Explanation

Radius equals half the diameter.

#3

What is the measure of an angle formed by the tangent and a chord intersecting outside a circle?

90 degrees
Explanation

Angle between tangent and chord is 90 degrees.

#4

In a circle with a radius of 6 units, what is the length of an arc intercepted by a central angle of 45 degrees?

3π units
Explanation

Length of arc equals radius times central angle in radians.

#5

In a circle with a radius of 5 units, what is the length of an arc intercepted by a central angle of 60 degrees?

3π units
Explanation

Length of arc equals radius times central angle in radians.

#6

What is the relationship between the measure of an inscribed angle and the measure of the central angle that intercepts the same arc?

They are always equal
Explanation

Inscribed angle equals the central angle.

#7

If the measure of an inscribed angle in a circle is 60 degrees, what is the measure of the intercepted arc?

120 degrees
Explanation

Intercepted arc equals twice the inscribed angle.

#8

What is the measure of the angle formed by two tangents drawn to a circle from an external point?

90 degrees
Explanation

Angle between tangents and radius is 90 degrees.

#9

In a circle with radius 6 units, what is the length of a chord that is perpendicular to the radius and has a distance of 4 units from the center?

4 units
Explanation

Chord equals twice the distance from center to perpendicular chord.

#10

In a circle with a radius of 8 units, what is the length of a chord that is 6 units away from the center?

6 units
Explanation

Chord equals twice the distance from center to non-perpendicular chord.

#11

In a circle with a radius of 5 units, what is the length of an arc intercepted by a central angle of 120 degrees?

15π units
Explanation

Length of arc equals radius times central angle in radians.

#12

If the length of an arc in a circle with radius 8 units is 12π units, what is the measure of the central angle that intercepts this arc?

150 degrees
Explanation

Central angle equals arc length divided by radius in radians.

#13

What is the measure of the central angle of a sector that has an arc length of 3π units in a circle with a radius of 5 units?

72 degrees
Explanation

Central angle equals arc length divided by radius in radians, converted to degrees.

#14

In a circle with radius 10 units, what is the area of the sector formed by a central angle of 120 degrees?

150π square units
Explanation

Area of sector equals half the product of radius squared and central angle in radians.

#15

In a circle with radius 12 units, what is the area of the segment formed by a central angle of 60 degrees?

24π square units
Explanation

Area of segment equals one-half the product of radius squared and the difference between two central angles in radians.

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