Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

The whole angle at the centre of a circle is :

Equal chords of a circle subtend equal angles at the centre.

Prove that the parallelogram circumscribing a circle is a rhombus.

Fill in the Blanks: Equal arcs of a circle subtend_____ angles at the centre.

Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Apply vectors to prove that if a pair of opposite sides of quadrilateral are equal and parallel, then the figure is a parallelogram.

Two parallel chords are drawn on the same side of the centre of a circle of radius R. It is found that they subtend and angle of theta and 2theta at the centre of the circle. The perpendicular distance between the chords is

Prove that supplementary of an angle is an obtuse angles.