Key Concepts:
- Definition of a Circle – A set of points in a plane equidistant from a fixed point (center).
- Radius – the distance from the center to any point on the circle. Diameter – twice the radius. Circumference – the perimeter of a circle, given by (C = 2\pi r).
- Central Angles & Arcs – A central angle has its vertex at the center. Congruent central angles correspond to congruent length of arcs.
- Arc Length – The measure of a portion of a circle's circumference, calculated as (L = \frac{\theta}{360^\circ} \cdot 2\pi r).
Skills Covered:
- Identifying congruent arcs using congruent central angles.
- Computing circumference and arc length given the radius and central angle.
Example Problem:
- A line cuts a circle of radius 5 into two arcs. If one arc has twice the length of another, find the length of the shorter arc.