Facts that Matter
CIRCLES AND ITS RELATED TERMS
The locus of a point which moves in a plane in such a manner that its distance from a given fixed point is always constant, is called a circle.
The fixed point is called the centre and constant distance is called the radius of the circle. In the figure, ‘O’ is centre and OP = r is a radius. We denote it by C(O, r).
A line segment, terminating (or having its end points) on the circle, is called a chord. A chord, passing through the centre is called a diameter of the circle. A line which intersects a circle in two distinct points is called a secant of the circle, whereas a line intersecting the circle in exactly one point is called a tangent to the circle.
In the figure, is a chord, is a diameter, is a secant and is a tangent to the circle at C.
I. Diameter is the longest chord in a circle.
II. Diameter = 2 x Radius
The length of the complete circle is called its circumference, whereas a piece of a circle between two points is called an arc.
I. A diameter of a circle divides it into two equal arcs, each of which is called a semicircle.
II. If the length of an arc is less than the semicircle, then it is a minor arc, otherwise, it is a major arc.
The region consisting of all points lying on the circumference of a circle and inside it is called the interior of the circle, whereas the region consisting of all points lying outside a circle is called the exterior of the circle.
The region consisting of all points which are either on the circle or lie inside the circle is called the circular region.
The part of the circular region bounded by an arc and its chord (including the chord and the arc), is called a segment of the circle. The segment containing the minor arc is called the minor segment whereas the segment containing the major arc is called the major segment.