Areas Related to Circles

• Basic Concepts
  • Perimeter (Circumference) $= 2\pi r$
  • Area of Circle $= \pi r^2$
  • Radius ($r$) and Diameter ($d$) relation: $d = 2r$
  • Value of $\pi \approx \frac{22}{7}$ or $3.14$
• Perimeter and Area of a Circle
  • Review of standard formulas
  • Applications in simple two-dimensional figures
  • Semi-circle properties and perimeter
• Areas of Sector and Segment of a Circle
  • Arc and its length $= \frac{\theta}{360^\circ} \times 2\pi r$
  • Sector of a Circle
    • Definition: Region enclosed by two radii and an arc
    • Area of Sector $= \frac{\theta}{360^\circ} \times \pi r^2$
    • Types: Minor Sector and Major Sector
  • Segment of a Circle
    • Definition: Region enclosed by a chord and an arc
    • Area of Segment $=$ Area of corresponding sector $-$ Area of corresponding triangle
    • Types: Minor Segment and Major Segment
• Areas of Combinations of Plane Figures
  • Composite figures involving circles, squares, rectangles, and triangles
  • Strategy:
    • Identify constituent geometric shapes
    • Add or subtract areas of regions accordingly
  • Common examples:
    • Circle inscribed in/circumscribed about a square
    • Flower beds, tracks, and arched windows
    • Regions bounded by arcs of circles