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 triangle Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the "hypotenuse" (side "c" in the figure). The sides adjacent to the right angle are called "legs" (or "catheti", singular: "cathetus"). Side "a" may be identified as the side "adjacent to angle B" and "opposed to" (or "opposite") "angle A", while side "b" is the side "adjacent to