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

Statement 1 : Two orthogonal circles intersect to generate a common chord which subtends complimentary angles at their circumferences. Statement 2 : Two orthogonal circles intersect to generate a common chord which subtends supplementary angles at their centers.

Prove that the area of a regular polygon hawing 2n sides, inscribed in a circle, is the geometric mean of the areas of the inscribed and circumscribed polygons of n sides.

Delta ABC is circumscribing a circle. Find the length of BC.

A circle passes through 3 vertices of a traingle. What is the centre of the circle called?

The side of a triangle inscribed in a given circle subtends angles alpha,betaa n dgamma at the centre. The minimum value of the arithmetic mean of cos(alpha+pi/2),cos(beta+pi/2) , and cos(gamma+pi/2) is equal to ____

Statement 1 represents Assertion, statement 2 represent Reasons . Statement I : One radian is the angle subtended at the center of a circle by an arc that is equal to the radius of the circle . Setement 2: Radian describes the planar angle subtended by a circular arc at the centre of the circle . Which one of the following statements is a correct statement ?

The angle subtend by a semicircle at the centre is _________.