#1
In a circle, what is the measure of a central angle that intercepts an arc equal in length to the radius of the circle?
60 degrees
ExplanationA central angle intercepting an arc equal in length to the radius forms an equilateral triangle, thus the angle measures 60 degrees.
#2
What is the relationship between the central angle of a circle and the arc it intercepts?
They are equal
ExplanationThe central angle and the intercepted arc are congruent in a circle.
#3
In a circle, what is the relationship between the measure of an inscribed angle and the intercepted arc?
The angle is half the arc
ExplanationAn inscribed angle's measure is half the measure of the intercepted arc.
#4
What is the measure of an inscribed angle formed by a chord that is half the length of the circle's diameter?
60 degrees
ExplanationA chord that is half the length of the diameter subtends an angle of 60 degrees at the center of the circle.
#5
In a circle, what is the relationship between the measure of a tangent-chord angle and the intercepted arc?
The angle is half the arc
ExplanationThe angle formed between a tangent and a chord is half the measure of the intercepted arc.
#6
What is the measure of a tangent-chord angle formed by a chord that is half the length of the circle's diameter?
45 degrees
ExplanationA tangent-chord angle formed by a chord half the length of the diameter is always 45 degrees.
#7
In a circle with radius 5 cm, what is the length of an arc intercepted by a central angle of 45 degrees?
2.5π cm
ExplanationThe length of the arc intercepted by a central angle can be calculated using the formula: (θ/360) * 2πr.
#8
If the diameter of a circle is 12 cm, what is the circumference of the circle?
24π cm
ExplanationCircumference of a circle is given by the formula: π * diameter.
#9
What is the measure of a central angle that forms an inscribed angle of 75 degrees?
150 degrees
ExplanationThe central angle is twice the measure of the inscribed angle.
#10
If an inscribed angle in a circle has a measure of 120 degrees, what is the measure of the intercepted arc?
240 degrees
ExplanationThe intercepted arc is twice the measure of the inscribed angle.
#11
If a tangent-chord angle in a circle has a measure of 30 degrees, what is the measure of the intercepted arc?
150 degrees
ExplanationThe intercepted arc is twice the measure of the tangent-chord angle.
#12
What is the measure of the tangent-chord angle that intercepts an arc of 135 degrees in a circle?
60 degrees
ExplanationThe tangent-chord angle is half the measure of the intercepted arc.
#13
What is the measure of the central angle in a circle with radius 8 cm that intercepts an arc of length 12 cm?
120 degrees
ExplanationUsing the arc length formula, the central angle can be found by rearranging: θ = (arc length / radius) * 180/π.
#14
What is the measure of the inscribed angle that intercepts an arc of 90 degrees in a circle?
90 degrees
ExplanationAn inscribed angle that intercepts a semicircle (90 degrees) is always a right angle.
#15
If the tangent-chord angle of a circle has a measure of 75 degrees, what is the measure of the intercepted arc?
300 degrees
ExplanationThe intercepted arc is twice the measure of the tangent-chord angle.
#16
What is the measure of an angle formed by a secant and a tangent if the intercepted arc is 150 degrees?
75 degrees
ExplanationThe angle formed by a secant and a tangent is half the measure of the intercepted arc.
#17
If the angle formed by a tangent and a chord intersecting at the point of tangency is 45 degrees, what is the measure of the intercepted arc?
45 degrees
ExplanationThe angle formed by a tangent and a chord is half the measure of the intercepted arc.