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
Cerebellopontine angle syndrome There are different defined degrees of surgical excision, termed 'subtotal resection', 'radical subtotal resection', 'near-total resection', and 'total resection' in order or increasing proportion of tumor removed. Lesser amount of tumor removal may increase likelihood of preservation of nerve function (hence better post-operative hearing), but also likelihood of tumor regrowth, necessitating additional treatment. The overall complication rate following surgery is around 20%; cerebrospinal fluid leak is the most common. Cerebellopontine angle syndrome The cerebellopontine angle syndrome is a distinct neurological syndrome of deficits that can arise due to the closeness of the cerebellopontine angle to specific cranial nerves. Indications include