#1
What is the measure of the central angle of a circle if it subtends an arc of 90 degrees?
60 degrees
ExplanationCentral angle = 1/2 * arc measure
#2
In a circle, what is the relationship between the radius and the diameter?
Radius = 1/2 * Diameter
ExplanationRadius is half of the diameter
#3
What is the measure of the central angle of a circle if it subtends an arc of 180 degrees?
90 degrees
ExplanationCentral angle subtending a semicircle is a right angle
#4
In a circle, what is the relationship between the circumference and the diameter?
Circumference = π * Diameter
ExplanationCircumference is π times the diameter
#5
What is the relationship between the central angle of a circle and the arc it subtends?
They are directly proportional
ExplanationCentral angle and subtended arc have a linear relationship
#6
In a circle, what is the relationship between the radius and the circumference?
Circumference = π * Radius
ExplanationCircumference is π times the radius
#7
What is the measure of an inscribed angle that intercepts a semicircle in a circle?
90 degrees
ExplanationInscribed angle intercepts a semicircle is a right angle
#8
What is the formula for finding the area of a sector of a circle?
A = r * θ
ExplanationArea of a sector = radius times central angle in radians
#9
What is the measure of a central angle of a circle if it subtends an arc of 45 degrees?
90 degrees
ExplanationCentral angle subtending half of a semicircle is a right angle
#10
What is the formula for finding the length of an arc in a circle?
L = r * θ
ExplanationLength of an arc = radius times central angle in radians
#11
What is the measure of the angle formed by two secants intersecting outside the circle?
Half the difference of intercepted arcs
ExplanationAngle = 1/2 * (larger arc - smaller arc)
#12
Which of the following is NOT a property of tangents to a circle?
The angle between the tangent and the chord is obtuse
ExplanationTangent and chord angle is never obtuse
#13
What is the relationship between the tangent and radius of a circle at the point of tangency?
Tangent * Radius = 1
ExplanationProduct of tangent and radius is constant at the point of tangency
#14
In a circle, if two chords are equal, then the corresponding arcs they subtend are:
Equal
ExplanationEqual chords subtend equal arcs
#15
What is the ratio of the area of a circle to the area of its circumscribed square?
1:π
ExplanationArea of circle to circumscribed square is in a ratio of 1 to π
#16
In a circle, if two chords are perpendicular to each other, what can be said about the product of their lengths?
Their product is always equal to the radius squared
ExplanationProduct of perpendicular chords' lengths equals the radius squared
#17
In a circle, if a chord is bisected by another chord, then what can be said about the product of the segments of the first chord?
Their product is always equal to the difference of the squares of the radii
ExplanationProduct of bisected chord segments equals difference of radii squares