Circles

A circle is a plane figure bounded by the curved line all points of which are the same distance away from the fixed point, called the centre. The length of the curved line, or the distance around the circle, is its-circumference. A straight line drawn from the centre to any point on the circumference is called a radius (plural: radii). OD the radios (see Fig. 19). The straight line that passes through the centre of the circle and both of whose ends are on the circumference is called a diameter. AB is the diameter. A line segment that connects any two points on the circumference of a circle is a chord. An example is BC.

Any part of curved line which makes the circle is an arc. The portion of the circle confined in AOD is a sector of the circle, for two sides are radii and the third side is an arc. Because its vertex is at the centre, angle AOD is a central angle.

When a circle is cut in half, each of the halves is called a semi­circle. When a circle is cut into four equal parts, each of the quarters is called a quadrant.

Area of a Circle. If a circle is divided into 4 quadrants and a square is circumscribed about the circle, four small squares are formed (Fig. 20). The side of each small square equal to the radius r. The area of each small square is r²; the area of the large square is equal to the sum of the four small squares, or 4r².

We can see that the area of the circle is about ¾ of the large square. It is approximately equal to 3 ¹/₇ of the small squares, or 3 ¹/₇ r². This can be also written πr².

Rule to remember: the area of a circle equals π, times the radius squared

A= πr².