48. Arcs of a Circle · Minor vs Major: The Circle's Split

Try to break it

Move A and B closer together. See how the top curve shrinks while the bottom curve grows? They are always partners, making up the whole circle.

How you build it

Draw a circle with a chord splitting two arcs.

• Draw a circle with centre O.
• Mark point A on the circumference.
• Mark point B on the circumference.
• Join point A and point B with a straight line to make the chord.

The proof, step by step

Prove that the minor arc and major arc together form the whole circle.

• An arc is a part of the circumference of a circle.
• A chord divides the circle into two arcs.
• The shorter arc is called the Minor Arc.
• The longer arc is called the Major Arc.

Worked example

In the given figure, a chord AB divides a circle into two arcs. If the length of arc APB is 12 cm and the length of the other arc is 20 cm, identify the major arc.

The major arc is defined as the longer part of the circumference. Since 20 cm is greater than 12 cm, arc AQB is the major arc.

• Arc APB
• Arc AQB — correct
• Both arcs are equal
• Cannot be determined