# Circle Geometry Properties

Can you find the numerous circle properties in the image? Click on the link to learn more.

- Radius is the same length: $OA = OC$
- Angle at center is twice angle at circumference: $2 \times \angle ABC = \angle AOC$.
- Inscribed angle theorem: $\angle ABC = \angle APC$.
- Thales' theorem: $\angle PAC = 90^ \circ$.
- Alternate segment theorem: $\angle ABC = \angle ACT$
- Perpendicular tangent theorem: $\angle OCT = 90 ^ \circ$.
- Tangents to the circle from a point have the same length: $TA = TC$.
- Opposite angles in a cyclic quadrilateral: $\angle ABC + \angle CDA = 180^ \circ$.

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.

## See Also

**Cite as:**Circle Geometry Properties.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/circle-geometry-properties/