ABCD is a rectangle. A circle passing through vertex C touches the sides AB and AD at M and N respectively. If the distance lof the line MN from the vertex C is P units then the area of rectangle ABCD is

A straight line is drawn through P(3,4) to meet the axis of x and y at Aa n dB , respectively. If the rectangle O A C B is completed, then find the locus of Cdot

ABCD is a rectangle and P,R and S are the mid - points of the AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

If vec a , vec ba n d vec c are the position vectors of the vertices A ,Ba n dC respectively, of A B C , prove that the perpendicular distance of the vertex A from the base B C of the triangle A B C is (| vec axx vec b+ vec bxx vec c+ vec cxx vec a|)/(| vec c- vec b|)dot

A circle with centre P . Line AB and line AC are tangents from point A at points B and C respectively . Which of the following is/ are true ?

ABCD is a rectangle with A as the origin. vec b and vec d are the position vectors of B and D respectively. (i) What is the position vector of C? (ii) If P, Q, R and S are midpoints of sides of AB, BC, CD and DA respectively, find the position vector of P, Q, R,S,

ABCD is a reactangular field .A vertical lamp post of height 12 m stands at the corner A. If the anngle of elevation of its top from B is 60^@ and from C is 45^@ , then the area of the field is

Two circles passing through A(1,2), B(2,1) touch the line 4x + 8y-7 = 0 at C and D such that ACED in a parallelogram. Then: coordinates of E are

A circle of radius 1 unit touches the positive x-axis and the positive y-axis at Aa n dB , respectively. A variable line passing through the origin intersects the circle at two points Da n dE . 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)

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Dela ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is

Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is A, then the value of (3A)/(2) is__.