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Questions and Answers
In a semicircle ABCD with center O, if arc AB is equal to arc CD and angle COD is 50, what is the measure of angle BOC?
In a semicircle ABCD with center O, if arc AB is equal to arc CD and angle COD is 50, what is the measure of angle BOC?
- 80 (correct)
- 110
- 100
- 130
In a circle with center O, angle AOC measures 160. What is the measure of angle COB?
In a circle with center O, angle AOC measures 160. What is the measure of angle COB?
- 160
- 100
- 80
- 200 (correct)
In a circle with center O, angle AOC is 160, AB = 28 cm and BC = 12 cm. Determine the ratio of chord AB to chord BC.
In a circle with center O, angle AOC is 160, AB = 28 cm and BC = 12 cm. Determine the ratio of chord AB to chord BC.
- 3:7
- 6:14
- 14:6
- 7:3 (correct)
In a circle, if two chords are equal in length, what can be inferred about their corresponding arcs?
In a circle, if two chords are equal in length, what can be inferred about their corresponding arcs?
In a given circle, if a central angle intercepts an arc of 80 degrees, what is the measure of the inscribed angle that intercepts the same arc?
In a given circle, if a central angle intercepts an arc of 80 degrees, what is the measure of the inscribed angle that intercepts the same arc?
If $\angle AOB$ is a central angle that subtends an arc of length 5$\pi$ cm in a circle with radius 10 cm, what is the measure of $\angle AOB$ in radians?
If $\angle AOB$ is a central angle that subtends an arc of length 5$\pi$ cm in a circle with radius 10 cm, what is the measure of $\angle AOB$ in radians?
A chord of length 10 cm is 12 cm away from the center of a circle. What is the radius of the circle?
A chord of length 10 cm is 12 cm away from the center of a circle. What is the radius of the circle?
What is the relationship between the diameter of a circle and the longest chord in the same circle?
What is the relationship between the diameter of a circle and the longest chord in the same circle?
Two parallel chords are drawn on opposite sides of the center of a circle. One chord has a length of 24 cm and is 5 cm from the center. If the radius of the circle is 13 cm, what is the length of the other chord?
Two parallel chords are drawn on opposite sides of the center of a circle. One chord has a length of 24 cm and is 5 cm from the center. If the radius of the circle is 13 cm, what is the length of the other chord?
If an inscribed angle in a circle intercepts a diameter, what is the measure of the inscribed angle?
If an inscribed angle in a circle intercepts a diameter, what is the measure of the inscribed angle?
Consider a circle with radius r. If the length of an arc is equal to the radius, what is the measure of the central angle subtended by the arc (in radians)?
Consider a circle with radius r. If the length of an arc is equal to the radius, what is the measure of the central angle subtended by the arc (in radians)?
If two circles are concentric, what can be said about their centers?
If two circles are concentric, what can be said about their centers?
In a circle with radius 6, a sector has an area of 6$\pi$. What is the central angle of this sector in radians?
In a circle with radius 6, a sector has an area of 6$\pi$. What is the central angle of this sector in radians?
What is the relationship between the angle formed by a tangent and a chord at the point of tangency, and the angle subtended by the chord in the alternate segment?
What is the relationship between the angle formed by a tangent and a chord at the point of tangency, and the angle subtended by the chord in the alternate segment?
Given a cyclic quadrilateral ABCD, if $\angle A = 80^\circ$, what is the measure of $\angle C$?
Given a cyclic quadrilateral ABCD, if $\angle A = 80^\circ$, what is the measure of $\angle C$?
Two secants from an external point A intersect a circle at points B, C, D, and E, such that AB = 6, AC = 15, AD = 5. What is the length of AE?
Two secants from an external point A intersect a circle at points B, C, D, and E, such that AB = 6, AC = 15, AD = 5. What is the length of AE?
A tangent PA and a secant PBC are drawn to a circle from an external point P. If PA = 8 cm and PB = 4 cm, find the length of the entire secant PC.
A tangent PA and a secant PBC are drawn to a circle from an external point P. If PA = 8 cm and PB = 4 cm, find the length of the entire secant PC.
In a circle with center O, chord AB is parallel to chord CD. If $\angle AOB = 70^\circ$, what is the measure of $\angle COD$?
In a circle with center O, chord AB is parallel to chord CD. If $\angle AOB = 70^\circ$, what is the measure of $\angle COD$?
A circle has a radius of 5cm. Find the length of an arc subtended by a central angle of 2.5 radians.
A circle has a radius of 5cm. Find the length of an arc subtended by a central angle of 2.5 radians.
Flashcards
What is an arc?
What is an arc?
An arc is a portion of the circumference of a circle.
What is a chord?
What is a chord?
A chord is a line segment that connects two points on a circle.
What is a central angle?
What is a central angle?
A central angle is an angle whose vertex is the center of a circle.
Equal arcs imply what about chords?
Equal arcs imply what about chords?
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Equal chords imply what about arcs?
Equal chords imply what about arcs?
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Study Notes
Section Test 11C: Relationships Among Angles, Arcs, and Chords
- In a semicircle ABCD with center O, arc AB is equal to arc CD, and angle COD is 50°.
- The task is to find the measure of angle BOC.
- O is the center of a circle.
- Angle AOC measures 160°.
- Arc AB measures 28 cm.
- Arc BC is 12 cm.
- Determine the measure of angle COB.
- Find the ratio of arc AB to arc AC.
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