Basic Geometrical Ideas - Circles

A circle is a simple closed curve where every point on the boundary is at an equal distance from a fixed point in the middle. Imagine a point $O$ in the center with a perfectly round boundary surrounding it.

The fixed point at the exact middle of the circle is called the Center. Any line segment joining the center to a point on the circle is called the Radius. Visually, if $O$ is the center and $P$ is on the boundary, the straight line $OP$ is the radius.

A Diameter is a line segment that passes through the center of the circle and has its endpoints on the circle's boundary. It is the longest chord of the circle and divides the circle into two equal parts called semicircles. It looks like a straight line cutting the circle exactly in half through the point $O$.

A Chord is any line segment joining two points on the circle. While a diameter is a chord that passes through the center, other chords may not. Visually, a chord is a straight line 'bridge' between two points on the curved boundary.

An Arc is a portion or a piece of the boundary of the circle. If you take a pair of scissors and cut a piece of the circle's perimeter, that curved part is an arc.

A Sector is the region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides. Visually, it looks like a slice of pizza or a pie cut from the center.

A Segment is a region in the interior of a circle enclosed by a chord and an arc. Unlike a sector, it does not necessarily touch the center; it looks like a portion 'sliced off' by a straight line chord.

The distance around the boundary of the circle is known as the Circumference. It represents the perimeter of the circular shape. If you were to unroll the circle into a straight line, its length would be the circumference.