Parts of a circle
- A chord is a segment whose endpoints are on the circle.
- A diameter is a chord through the center; it's twice the radius and the longest possible chord.
- A secant is a line that crosses the circle at two points.
- A tangent is a line in the plane of the circle that touches it at exactly one point, the point of tangency.
Central angles and arcs
A central angle has its vertex at the center. The arc it cuts off has the same measure in degrees as the angle.
- A minor arc is less than \(180°\) and is named with two letters: \(\overset{\frown}{AB}\).
- A major arc is more than \(180°\) and is named with three letters: \(\overset{\frown}{ACB}\).
- A semicircle is exactly \(180°\).
A central angle of \(80°\) cuts off a minor arc of \(80°\); the corresponding major arc measures \(360° - 80° = 280°\).
Inscribed angles
An inscribed angle has its vertex on the circle and its sides are chords. The arc inside the angle is its intercepted arc.
Tangents
Chords
The second fact gives a way to find the center of a circle: draw two chords and their perpendicular bisectors. They cross at the center.
Practice
Quick check
An inscribed angle intercepts a semicircle. What is its measure?
A semicircle measures \(180°\), and the inscribed angle is half of that.
Quick check
What angle does a tangent make with the radius at the point of tangency?
A tangent is always perpendicular to the radius at the point of tangency.