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,

Condition For Leaving The Circle

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

If the tangents AB and AQ are drawn from the point A(3, -1) to the circle x^(2)+y^(2)-3x+2y-7=0 and C is the centre of circle, then the area of quadrilateral APCQ is :

From the point P(16,7), tangents PQ and PR are drawn to the circle x^(2)+y^(2)-2x-4y-20=0 If C is the centre of the circle,then area of quadrilateral PQCR is