Circles and Their Special Parts

A circle is a set of all points the same distance from a center point. Circles have unique properties and special lines and segments associated with them, like chords, tangents, and secants.

• Radius: A line from the center to any point on the circle.
• Diameter: A straight line passing through the center, touching two points on the edge (twice the radius).
• Chord: A line segment with both endpoints on the circle.
• Tangent: A line that touches the circle at exactly one point.

Important Theorems

• The angle in a semicircle is always a right angle (\(90^\circ\)).
• Tangents from a common external point to a circle are equal in length.

Why Circles Matter

Circles are everywhere—from wheels to clocks to pizzas! Their properties help us design roundabouts, gears, and even study planetary orbits.