Interior Angle Of A Circle

An angle is inside a circle when the vertex lies anywhere inside the circle.

Interior angle of a circle. Intersecting chords angle theorem. The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs. Angle inscribed in semicircle is 90.

The inscribed angle theorem states that an angle o inscribed in a circle is half of the central angle 2o that subtends the same arc on the circle. The sides of the angle lie on the intersecting lines. The opposite angles of a cyclic quadrilateral are supplementary.

The central angle of a circle is twice any inscribed angle subtended by the same arc. An angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

The interior angles of a triangle add up to 1800. An interior angle has its vertex at the intersection of two lines that intersect inside a circle. In the figure below angle caf is an interior angle of the circle with centre o.

M textrm caf frac textrm m widehat textrm be space space textrm m widehat textrm cf 2. What are the relationships between measures of angles formed by intersecting secants tangents or secant tangents outside of a circle and their intercepted arcs. The measure of an interior angle is the average of the measures of the two arcs that are cut out of the circle by those intersecting lines.

Circle theorems gcse maths higher duration. Central angles subtended by arcs of the same length are equal.