Circle: A circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point in the plane is always constant.Interior and Exterior of a circle: Let C(O, r) be a given circle. A point P is said to lie inside, outside or on the given circle according as OP < r, OP > r or OP = r respectively. All the points lying inside a circle are called its interior points and all those points which lie outside the circle are called its exterior points.
Circular region: The set of all points lying inside and on the circle C(O, r) is called a circular region .
Circumference of a circle: The perimeter of a circle is called its circumference.
Chord of a circle: A line segment joining two points on a circle is called the chord of the circle.
In the figure AS is the chord of a circle.
A chord passing through the centre of the circle is called a diameter of the circle.
Clearly, diameter = 2 ×radius.
Congruence of circle: Two circles are said to be congruent if their radii are equal.
Arc of a circle: A continuous part of the circumference of a circle is called 'an arc of a circle.
The arc PAO will be called a minor arc if l(PAO) < l(PBO) and will be called a major arc if l(PAO) > l(PBO).
Semi-circle: A diameter divides the circle into two equal arcs. Each of the two arcs is called a semi-circle.
Central angle: Let C(O, r) be any circle. Then any angle whose vertex is 0 is called a central angle.
Degree measure of an arc: The degree measure of an arc is the measure of the central angle containing the arc.
Congruent arcs: Two arcs of a circle (or of congruent circles) are congruent if the degree measure of the two arcs are the same.
Thus arc AB arc CD if ÐAOB = ÐCOD and AOB = ÐCOD
Þ arc AB:; CD.
Segment of a circle: Let AB be a chord of the circle C (O, r). Then AB divides the circular disc into two parts. Each part is called a segment of the circle.
The segment containing the minor arc is called the minor segment and the segment containing the major arc is called the major segment of the circle.
The minor and major segments of a circle are called the alternate segments of each other.
Sector: A sector is that region of a circular disc C(O, r) which lies between an arc and the two radii joining the extremities of the arc and the centre .
Secant of a circle: A line which intersects a circle in two distinct points is called a secant of the circle.
Tangent to a circle: A line is called a tangent line if it passes through two coincident points on the circle.
The point at which the tangent intersects the circle is called the point of contact.
Concentric circle: Circles having the same centre and with varying radii are known as concentric circles.
Cyclic quadrilateral: If all the four vertices of a quadrilateral, as in the figure below, lie on a circle, then such a quadrilateral is called a cyclic quadrilateral. If four points lie on a circle, then they are said to be concyclic.
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