ABCD is a quadrilateral. AP is a line segment drawn through A and parallel to the diagonal BD, which intersects extended CD at P. If the area of the quadrilateral be 22 sq.cm, then find the value of `1/2DeltaBCP`.

The diagonals of a square ABCD intersect at O. If the length of each sides of the square is 6cm then find the value of OA^2+OB^2+OC^2+OD^2 .

In DeltaABC a straight line parallel to BC intersects the sides AB and AC at the points P and Q respectively. If AP=QC , AB=12cm , AQ=2cm , then find the value of CQ .

A circle of radius 1 unit touches the positive x-axis and the positive y-axis at A and B , respectively. A variable line passing through the origin intersects the circle at two points D and E . If the area of triangle D E B is maximum when the slope of the line is m , then find the value of m^(-2)

ABCD is a square of side l . A line parallel to the diagonal BD at a distance 'x' from the vertex A cuts two adjacent sides. Express the area of the segment of the square with A at a vertex, as a function of x. Find this area at x=1//sqrt(2) and at x=2 , when l=2 .

A straight line drawn through D of the parallelogram ABCD intersects AB and the extended part of CB at the points E and F respectively. Prove that AD:AE=CF:CD .

Let A B C D be a quadrilateral with area 18 , side A B parallel to the side C D ,a n dA B=2C D . Let A D be perpendicular to A Ba n dC D . If a circle is drawn inside the quadrilateral A B C D touching all the sides, then its radius is a = 3 (b) 2 (c) 3/2 (d) 1

A line through point A(1,3) and parallel to the line x-y+1 = 0 meets the line 2x-3y + 9 = 0 at point P. Find distance AP without finding point P.

In the isosceles right-angled DeltaABC,angleA=90^@ . ADbotBC and the line segment through D and parallel to BA intersects AC at a point E. If DE = 2 cm, then BC =

If a circle passes through the points of intersection of the coordinates axes with the lines lambdax-y+1=0 and x-2y+3=0 , then find the value of lambda .