MATH theorem

Arc Measure

The measure of an arc in degrees, dependent on the central angle and located at the center of a circle.

Arc Length

The actual length measure of an arc, dependent on a central angle, and expressed in units of length like centimeters or inches.

Arc Addition Theorem

The sum of two adjacent arc measures formed by arcs.

Central Angle Theorem

The measure of a central angle is equal to the measure of its intercepted arc.

Inscribed Angle Theorem

The half measure of the central angle subtended in the same arc.

Semicircle Theorem

An inscribed angle intercepting the diameter of a semicircle with a measure of 90°.

Bisected Chord Theorem

If the diameter is perpendicular to a chord, it bisects the chord and its arc.

Intersecting Chord Theorem

The product of segments of intersecting chords is equal.

Chord Angle Theorem

The angle formed by intersecting chords is half the sum of the intercepted arcs' measures.

Secant

A line intersecting a circle at two points and containing a chord of the circle.

Tangent

A straight line touching the circle's circumference at one point.

Secant Tangent Theorem

The angle formed by a secant and tangent at the point of tangency is half the intercepted arc's measure.

Two Secant Theorem 1.1

The angle formed by two intersecting secants inside a circle is half the sum of the intercepted arcs' measures.

Two Secant Theorem 1.2

The angle formed by two secants or a secant and a tangent outside a circle is half the positive difference of the intercepted arcs' measures.

Two Tangent Theorem

The angle formed by two tangents from a point outside the circle is half the difference of the intercepted arcs' measures.

Tangent-Secant Segment Theorem

The square of a tangent segment's length equals the product of the secant segment's length and its external segment.