Circles

Fold unfold A B AB divides the circle into equal halves. AB is a diameter of the circle

A B O C Fold the paper circle in half in another way to obtain another diameter of the circle. The two lines meet at point O. O is the centre of the circle. The line OC is the radius of the circle.

Definitions The diameters of a circle pass through the centre of the circle. The diameter of a circle is twice its radius Diameter = 2  Radius Radius = Diameter  2

Perimeter of circle A B The circumference of a circle is slightly longer than 3 times its diameter. d This approximate value, 3.14 is represented by . We read  as ‘pi’. Circumference of a circle =   Diameter =  d

Perimeter of semi-circle d Circumference of a circle =  d Perimeter of a semi-circle =   Radius + Diameter = r + d

Perimeter of quarter-circle Circumference of a circle =  d Perimeter of a semi-circle =   Radius + Diameter = r + d Perimeter of quadrant = r + 2r

Area of circle A circle is drawn on a 1-cm square grid. Radius of circle = 10 cm Area of quarter circle = 76 cm2 Area of circle = 4 x 72 = 304 cm2

Area of circle Cut the circle into 24 equal pieces.

Area of circle Rearrange 23 pieces like this.

Area of circle Area of circle =   r  r Cut the last piece into halves and place one half at each end. The pattern looks like a rectangle. Area of circle =   r  r

Shapes with the same area The figure below is formed by a semicircle and two quarter circle.

Shapes with the same area Area of the figure = 20 cm  10 cm = 200 cm2

Shapes with the same area ACDF is a rectangle made up of 2 squares.

Shapes with the same area The figure shows semi-circles of equal areas at the sides of a square.

Shapes with the same area Four identical circles of diameter 10 cm are arranged in a big circle.