Circles - Secants, Tangents and Angles

A secant is a line that intersects a circle at two points.

A tangent line is a line that touches a circle at exactly one point.

The angle formed between a tangent and a chord through the point of contact is equal to the measure of the opposite arc.

The inscribed angle is half the measure of the intercepted arc.

The measure of the angle is equal to half the difference of the measures of the intercepted arcs.

The length of the tangent segment is the square root of the difference between the square of the distance from the point to the center and the square of the radius.

The area of a circle is A = πr², where r is the radius.

The circumference of a circle is C = 2πr, where r is the radius.

The opposite angles of an inscribed quadrilateral are supplementary (add up to 180°).

The measure of each angle is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.