Lesson 14: Introduction to Circles part 1

Circle:

A set of all points in a plane that are equidistant from a fixed point called the center.

Center:

The fixed point inside the circle from which all points on the circumference are equidistant.

Radius (plural: Radii):

A line segment connecting the center of the circle to any point on the circumference. Its length is denoted by 'r'.

Diameter:

A line segment passing through the center of the circle whose endpoints lie on the circumference. Its length is twice the radius (d = 2r).

Chord:

A line segment whose endpoints both lie on the circumference of the circle. The diameter is the longest possible chord.

Circumference:

The distance around the boundary of the circle. Formula: $ C = 2\pi r $ or $ C = \pi d $.

Arc:

A portion of the circumference of a circle.

• Minor Arc: An arc shorter than a semicircle.
• Major Arc: An arc longer than a semicircle.
• Semicircle: An arc that is exactly half of the circle (formed by a diameter).

Tangent:

A line that touches the circle at exactly one point (the point of tangency). A tangent is perpendicular to the radius at the point of tangency.

Secant:

A line that intersects the circle at exactly two points.

Segment:

The region bounded by a chord and the arc subtended by the chord.

• Minor Segment: The smaller region bounded by a chord and the minor arc.
• Major Segment: The larger region bounded by a chord and the major arc.

Sector:

The region bounded by two radii and the arc between their endpoints on the circumference.

• Minor Sector: The smaller region bounded by two radii and the minor arc.
• Major Sector: The larger region bounded by two radii and the major arc.

Concentric Circles:

Circles that share the same center but have different radii.

Area of a Circle:

The space enclosed by the circumference. Formula: $ A = \pi r^2 $.