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
Right ascension of objects in the sky. For example, if a star with RA = is at its meridian, then a star with RA = will be on the/at its meridian (at its apparent highest point) 18.5 sidereal hours later. Sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Usually measured in degrees (°), it is the complement of right ascension with respect to 24. It is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian.