Circle Properties Quiz

Circle Properties

• A circle is a collection of points in a plane that are equidistant from a fixed point, called the center.
• Equal chords of a circle (or congruent circles) subtend equal angles at the center.
• If the angles subtended by two chords of a circle (or congruent circles) at the center are equal, the chords are equal.

Chord Properties

• The perpendicular from the center of a circle to a chord bisects the chord.
• The line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
• Equal chords of a circle (or congruent circles) are equidistant from the center (or corresponding centers).
• Chords equidistant from the center (or corresponding centers) of a circle (or congruent circles) are equal.

Arc and Chord Relationships

• If two arcs of a circle are congruent, then their corresponding chords are equal.
• If two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.
• Congruent arcs of a circle subtend equal angles at the center.

Angle Properties

• The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
• Angles in the same segment of a circle are equal.
• An angle in a semicircle is a right angle.

Cyclic Quadrilaterals

• If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.
• The sum of either pair of opposite angles of a cyclic quadrilateral is 180.