Can you find the numerous circle properties in the image? Click on the link to learn more.
- Radius is the same length:
- Angle at center is twice angle at circumference: .
- Inscribed angle theorem: .
- Thales' theorem: .
- Alternate segment theorem:
- Perpendicular tangent theorem: .
- Tangents to the circle from a point have the same length: .
- Opposite angles in a cyclic quadrilateral: .
Here are additional basic properties that are useful to know:
- Equal arcs subtend equal angles and vice versa.
- Equal angles stand on equal chords and vice versa.
- Equal chords are equidistance from the center and vice versa.
- The perpendicular bisector of a chord passes through the center of the circle
- Any three non-colinear points lie on a unique circle.
- Tangent-chord theorem
- Two secants theorem
- The line connecting intersection points of two circles is perpendicular to the line connecting their centers.