Inscribed angle its intersection points equals half of the central angle subtended by the chord. See also Tangent lines to circles. The inscribed angle theorem is used in many proofs of elementary Euclidean geometry of the plane. A special case of the theorem is Thales' 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 quadrilaterals 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
Solid angle of its faces is one-sixth of that, or sr. Solid angles can also be measured in square degrees (1 sr = () square degrees), in square minutes and square seconds, or in fractions of the sphere (1 sr = fractional area), also known as spat (1 sp = 4 sr). In spherical coordinates there is a formula for the differential, where is the colatitude (angle from the North pole) and is the longitude. The solid angle for an arbitrary oriented surface S subtended at a point P is equal to the solid angle of the projection of the surface S