Circles and composite areas — Fundamentals of Circles + 5 more topics

When tackling complex composite areas, especially those involving circles, the main challenge is dissecting the figure into manageable parts. These parts usually include circles, semicircles, quarter circles, sectors, triangles, squares, and rectangles. You'll either sum the areas of these parts or subtract the area of one part from another.

• Center: The middle point of the circle. We often label it using its coordinates, like (h, k).
• Radius (r): The distance from the center to any point on the circle's edge. Think of it as half the circle's width.
• Diameter (d): The distance across the circle, passing directly through the center. It's always twice the radius (d = 2r).
• Chord: A straight line segment connecting any two points on the circle's edge. The diameter is the longest possible chord.
• Secant: A line that passes through a circle, intersecting it at two points.
• Tangent: A line that touches the circle at exactly one point, called the point of tangency. This line is always perpendicular to the radius at that point.
• Circumference (C): The total distance around the circle's edge. It's like the perimeter of other shapes.
• Area (A): The amount of space enclosed within the circle.