Arcs & Sectors | Mathematics for GCSE/IGCSE - Class 10 PDF Download

What is an arc?

• An arc is a portion of the circle's circumference.
• Two points on a circle's circumference will form two arcs.
• The smaller arc is called the minor arc, while the larger one is known as the major arc.

What is a sector?

• In technical language, a sector refers to the portion of a circle that is enclosed by two radii and an arc.
• It's simpler to envision a sector as resembling a slice of circular pizza, cake, or pie, with the arc representing the curved edge (similar to the crust).
• When two radii are drawn within a circle, they form two sectors.
  • The smaller sector is termed the minor sector, while the larger one is called the major sector.
• If the angle of the slice is represented by θ (the Greek letter "theta"), then the formulas for the sector's area and the arc's length are fractions derived from the circle's area and circumference.
• It's important to note that a complete circle comprises 360°, thus the fraction signifies the angle out of 360°.

• If memorizing formulas isn't your forte, there's a rationale behind these two.
  • It's essential to recall the formulas for circumference and area.
  • Subsequently, the process involves determining a fraction of the entire circle – denoted as "θ out of 360."
• Utilizing sector and arc formulas follows a similar logic to any other formulaic approach.
  • Jot down what you're aware of and what you aim to ascertain.
  • Select the appropriate formula.
  • Substitute the known values and solve for the desired outcome.