gen-define-properties-of-circles-and-give-one-short-worked-examp-99b3

Define properties of circles and give one short worked example.

# Properties of Circles ## Key Definitions - **Center**: Fixed point equidistant from all points on the circle - **Radius (r)**: Distance from center to any point on the circle - **Diameter (d)**: Distance across circle through center; d = 2r - **Circumference (C)**: Distance around the circle; C = 2πr = πd - **Area (A)**: Space enclosed by circle; A = πr² ## Important Properties 1. All radii of the same circle are equal 2. A diameter divides a circle into two equal semicircles 3. The longest chord is the diameter 4. A tangent line touches the circle at exactly one point and is perpendicular to the radius at that point 5. All points on a circle are equidistant from the center --- ## Worked Example **Problem**: A circle has a radius of 5 cm. Find its circumference and area. **Solution**: - Given: r = 5 cm - Circumference: C = 2πr = 2π(5) = 10π ≈ **31.42 cm** - Area: A = πr² = π(5)² = 25π ≈ **78.54 cm²**