## 9 Questions

A circle is the collection of all points in a plane, which are equidistant from a fixed point called the ______

centre

Equal chords of a circle (or of congruent circles) subtend equal angles at the ______

centre

If the angles subtended by two chords of a circle (or of congruent circles) at the centre (corresponding centres) are equal, the chords are ______

equal

The perpendicular from the centre of a circle to a chord ______ the chord

bisects

The line drawn through the centre of a circle to bisect a chord is ______ to the chord

perpendicular

Equal chords of a circle (or of congruent circles) are equidistant from the ______ (or corresponding centres)

centre

Chords equidistant from the centre (or corresponding centres) of a circle (or of congruent circles) are ______

equal

If two arcs of a circle are congruent, then their corresponding chords are ______

equal

Congruent arcs of a circle subtend equal angles at the ______

centre

## Study Notes

### 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.

Test your knowledge on various properties of circles such as equal chords, angles subtended by chords, perpendicular bisectors, and more.

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