Circle Properties and Theorems Quiz

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.

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.