Student Projects/Circles

CIRCLES

In our daily life we see many geometrical shapes around us and circle is among the most common. We can see circles in the boundaries of the clock, plates, bangles, rings and so many more of our daily life objects. In the past the invention of wheel itself is an application of the properties of the circle. Circle is defined as the collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane. The fixed point is called as the Centre of the circle and the fixed distance is called as the radius of the circle.

TERMS RELATED TO A CIRCLE

A circle divides the plane on which it lies into three parts:- • Interior of the circle • Exterior of the circle • The circle itself

CHORD

A line segment whose end points lie on the circle is called a chord. A chord which passes through the centre is called as the diameter of the circle. Diameter is twice the length of a radius. The diameter is the longest chord.

ARC

A piece of circle between two points is called an arc. The smaller piece is called minor arc and the larger piece is called major arc. If AB are the ends of a diameter, then both the arcs are equal and are called as a semicircle.

SEGMENT

The region between a chord and either of its arc is called as a segment. the larger region is called as major segment while the smaller region is called the minor segment.

SECTOR

The region between an arc and two radii joining the centre to the end points of the arc is called a sector. The larger region is the major sector while the smaller region is the minor sector.

PROPERTIES AND THEOREMS OF A CIRCLE

• Equal chords of a circle subtend equal angles at the centre of the circle.

• The perpendicular from the centre of the circle to a chord bisects the chord.

• There is one and only one circle passing through three given non collinear points.

• Equal chords of a circle are equidistant from the centre of a circle.

• The angle subtended by an arc at the centre of a circle 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.

• 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( they are concyclic).

• Angle in a semicircle is a right angle.