Podcast Beta
Questions and Answers
Explain the relationship between equal chords and their angles at the center of a circle.
Equal chords of a circle (or of congruent circles) subtend equal angles at the centre.
What happens when the angles subtended by the chords of a circle at the center are equal?
If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
What is the property of the perpendicular drawn from the centre of a circle to a chord?
The perpendicular drawn from the centre of the circle to a chord bisects the chord.
Describe the relationship between equal chords and their distance from the center of a circle.
Signup and view all the answers
What is the relationship between congruent arcs and the angles they subtend at the center of a circle?
Signup and view all the answers
What is the property of equal chords of a circle?
Signup and view all the answers
What is the property of the perpendicular drawn from the centre of a circle to a chord?
Signup and view all the answers
What is the property of chords equidistant from the centre of a circle?
Signup and view all the answers
What is the property of congruent arcs of a circle?
Signup and view all the answers
What is the property of the angle subtended by an arc at the centre?
Signup and view all the answers
Study Notes
Relationship Between Equal Chords and Angles at the Center
- Equal chords in a circle subtend equal angles at the center.
- If two chords are equal, the angles subtended by these chords at the center will also be equal.
Angles Subtended by Chords at the Center
- When the angles subtended by the chords of a circle at the center are equal, the corresponding chords are equal in length.
- This property assists in determining the equality of chords without direct measurement.
Perpendicular from the Center to a Chord
- A perpendicular drawn from the center of a circle to a chord bisects the chord.
- This means that the two segments created by the perpendicular line are equal in length.
Equal Chords and Distance from the Center
- Equal chords of a circle are located at equal distances from the center.
- If two chords are equal, the perpendicular distance from the center to each chord will also be the same.
Congruent Arcs and Angles Subtended at the Center
- Congruent arcs in a circle subtend equal angles at the center.
- This indicates a direct relationship between the arcs' lengths and the angles they form at the center.
Property of Equal Chords
- Equal chords are equidistant from the center of the circle.
- This relationship emphasizes the symmetry in the circle concerning its center.
Perpendicular from Center to Chord (Property Recap)
- The line from the center to the chord that is perpendicular bisects the chord into two equal parts.
- This property holds true for all chords within the circle.
Chords Equidistant from the Center
- Chords that are equidistant from the center of a circle are equal in length.
- This property reinforces the connection between the center and the positioning of the chords.
Property of Congruent Arcs
- Congruent arcs in a circle are equal in length and subtend equal angles at the center.
Angles Subtended by Arc at the Center
- The angle subtended by an arc at the center of a circle is unique to that arc.
- This angle influences the dimensions and relationships of the corresponding chords and arcs within the circle.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of circle properties and theorems with this quiz. Explore concepts such as radius, diameter, chord, segment, and cyclic quadrilateral. Discover the relationships between angles subtended by chords, equal chords, and the perpendicular bisector theorem.
