Study Notes
A circle is a plane figure enclosed by a curved line, with every point on the line equidistant from a point within, called the center.
- Radius — the distance from the center to the curve of the circle. Example: In a circle with a center at point O, if the radius is 5 cm, then every point on the circle is 5 cm from O.
- Circumference — the boundary of a circle. Example: The circumference of a circle with radius 7 cm is approximately 44 cm.
- Diameter — any straight line passing through the center and touching the circumference at each end, equal to twice the radius. Example: If the radius is 4 cm, the diameter is 8 cm.
- Arc — a portion of the circumference of a circle. Example: In a circle, the arc from point P to Q is a minor arc, while the arc from Q to R is a major arc.
- Sector — a region enclosed by two radii and an arc. Example: A sector with a central angle of 60° in a circle with radius 10 cm.
Exam Tips
Key Definitions to Remember
- Radius: The distance from the center to the edge of the circle.
- Diameter: A line that passes through the center and touches the circle at two points.
- Circumference: The total distance around the circle.
- Arc: A part of the circumference.
- Sector: A 'slice' of the circle, defined by two radii and an arc.
Common Confusions
- Confusing radius with diameter; remember, the diameter is twice the radius.
- Mixing up arc and sector; an arc is just the curved line, while a sector includes the area.
Typical Exam Questions
- What is the circumference of a circle with a radius of 12 cm? Use the formula C = 2πr to find the circumference.
- How do you find the area of a sector with a central angle of 60° and radius 10 cm? Use the formula for the area of a sector: (θ/360) × πr².
- What is the length of an arc with a central angle of 90° in a circle with radius 5 cm? Use the formula for arc length: (θ/360) × 2πr.
What Examiners Usually Test
- Ability to calculate circumference and area of circles.
- Understanding the relationship between radius, diameter, and circumference.
- Calculating the length of arcs and area of sectors.