Circle Theorems

Alternate segment theorem

The angle at the centre is twice the angle at the circumference

Angles in the same segment are equal.

The angle in a semicircle is 90 degrees.

The angle between a tangent and a radius is 90 degrees. Tangents which meet at the same point are equal in length.

The opposite angles in a cyclic quadrilateral total 180 degrees.

The perpendicular from the centre of a circle to a chord bisects the chord

Central Angle

Angle with its vertex at the center of a circle

Central Angles Sum

Total sum of central angles in a circle is 360 degrees

Arc

A portion of a circle defined by two endpoints

Semicircle

An arc with a measure equal to 180 degrees

Minor Arc

An arc with a measure less than 180 degrees

Major Arc

An arc with a measure greater than 180 degrees

Adjacent Arcs

Arcs in a circle sharing exactly one common point

Arc Length

Distance between two endpoints along an arc in linear units

Sector Area

Ratio of the area of a sector to the area of the whole circle

Inscribed Angle

Angle with its vertex on a circle and sides containing chords

Intercepted Arc

Arc with endpoints on the sides of an inscribed angle

Congruent Arcs

Arcs with the same measure in the same or congruent circles

Inscribed Polygon

Polygon where each side is tangent to a circle circumscribed around it

Tangent

A line that intersects a circle at exactly one point

Common Tangent

Line, ray, or segment tangent to two circles in the same plane

Two-Tangent Theorem

If two segments from the same exterior point are tangent to a circle, they are congruent

Circumscribed Polygon

Polygon with each side tangent to a circle inscribed within it

A Tangent

It is a straight line that touches the circumference of the circle at only one point.

Congruent

To have the same shape and size