Editing Inscribed angle (section)

==Applications==
[[File:cyclic_quadrilateral_supplementary_angles_visual_proof.svg|thumb|class=skin-invert-image|[[Proof without words]] using the inscribed angle theorem that opposite angles of a [[cyclic quadrilateral]] are supplementary:<br />2𝜃 + 2𝜙 = 360° ∴ 𝜃 + 𝜙 = 180°]]
The inscribed angle [[theorem]] is used in many proofs of elementary [[Euclidean geometry of the plane]].  A special case of the theorem is [[Thales's theorem]], which states that the angle subtended by a [[diameter]] is always 90°, i.e., a right angle.  As a consequence of the theorem, opposite angles of [[cyclic quadrilateral]]s sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle.  As another example, the inscribed angle theorem is the basis for several theorems related to the [[power of a point]] with respect to a circle. Further, it allows one to prove that when two chords intersect in a circle, the products of the lengths of their pieces are equal.