Condition for which circle can be drawn in quadrilateral

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Find the area of quadrilateral PQOR,

Let ABCD be a quadrilateral in which AB is parallel to CD and perpendicular to AD, AB = 3CDand the area of the quadrilateral is 4 square units. If a circle can be drawn touching all the sides of the quadrilateral, then its radius is:

12points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points ?

Let ABCD be a quadrilateral in which AB is parallel to CD and perpendicular to AD,AB =3 3CDand the area of the quadrilateral is 4 square units.If a circle can be drawn touching all the sides of the quadrilateral,then its radius is:

PA and PB are the two tangents drawn on a circle from and external point P. The centre of the circle is O and the tangents touches the circles at points A and B. Then quadrilateral OAPB is-

Consider the following statements: (i) Infinitely many circles can be drawn touching two parallel lines.( ii).Exactly four circles can be drawn touching two intersecting lines.(iii). Exactly one circle can be drawn touching three lines,not being concurrent.The true statements are:

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC. or A circle touches all the four sides of a quadrilateral ABCD. Prove that AB+CD=BC+DA.