A circle touches the sides of a quadrilateral `A B C D` at `P ,\ Q ,\ R ,\ S` respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.

A circle touches all the four sides of a quadrilateral A B C D . Prove that: A B+C D=B C+D A .

Find the area of a quadrilateral A B C D\ whose sides are 9\ m ,\ 40\ m ,\ 28\ m\ a n d\ 15\ m respectively and the angle between the first two sides is a right angle.

The diagonals of a quadrilateral A B C D are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

The diagonals of a quadrilateral A B C D are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

A circle is touching the side B C of A B C at P and touching A B and A C produced at Q and R respectively. Prove that A Q=1/2(P e r i m e t e r\ of\ A B C) .

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

A circle touches two of the smaller sides of a DeltaABC(a lt b lt c) and has its centre on the greater side. Then, find the radius of the circle.

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

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

In Figure, A B C D is a quadrilateral. Name a pair of adjacent sides. Name a pair of opposite sides. How many pairs of adjacent sides are there? How many pairs of opposite sides are there? Name a pair of adjacent angles. Name a pair of opposite angles. How many pairs of adjacent angles are there? How many pairs of opposite angles are there?