![]() Include the relationship between central, inscribed, and circumscribed angles inscribed angles on a diameter are right angles the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Theorem In the same or congruent circles, if two central angles are congruent, their arcs are congruent. Proof O is the centre of the circle By Theorem 1 y An inscribed angle is an angle whose vertex lies on the circle and whose sides contain chords of a circle. Theorem 4 The opposite angles of a quadrilateral inscribed in a circle sum to two right angles The opposite angles of a cyclic quadrilateral are supplementary. Inscribed Quadrilateral Theorem: A quadrilateral can be inscribed in a circle if and only if the opposite angles.Ī quadrilateral which can be inscribed in a circle is called a cyclic quadrilateral. Circle Theorem for Arcs and Chordsįor inscribed quadrilaterals in particular, the opposite angles will always be supplementary. An inscribed polygon is a polygon where every vertex is on the circle, as shown below. Equal angles subtended at the centre of a circle cut off equal chords. Equal chords subtend equal angles at the centr e of a circle. If two arcs subtend equal angles at the centre of a circle, then the arcs are equal. ![]()
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