An inscribed angle is formed when 2 secant lines of a circle intersect on circle. An inscribed angle is to intersect an arc on the circle. The arc is the portion of the circle which is in the interior of the angle. The measure of intercepted arc (equal to its central angle) is exactly twice the measure of inscribed angle.

The inscribed angle theorem states that an angle θ inscribed in the circle is half of the central angle 2θ which subtends the same arc on the circle. Thus, the angle does not change as its apex is moved to different positions on the circle. The inscribed angle is defined for points on the major arc. Geometrically an inscribed angle is formed when 2 secant lines of a circle (or, in the degenerate case, when 1 secant line and 1 tangent line of that circle) intersect on the circle. Geometrically, an inscribed angle is formed when 2 secant lines of a circle (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.

It is easiest to think of an inscribed angle as being defined by 2 chords of the circle sharing an endpoint. An inscribed angle is said to intersect an arc on circle. The arc is the portion of the circle which is in the interior of the angle. The measure of intercepted arc is exactly twice the measure of inscribed angle.

This single property has many consequences within the circle. For instance, it allows one to prove that when 2 chords intersect in a circle, the products of the lengths of their pieces are equal. It allows one to prove that the opposite angles of a cyclic quadrilateral are supplementary.

While central angles are formed by radii, inscribed angles are formed by chords. The measure of the inscribed angle is half the measure of the intercepted arc of it. Inscribed angles subtended by same arc of a circle are equal. Inscribed angles subtended by same arc of a circle are equal. An angle inscribed in a circle has half the angle measure of corresponding central angle.