Let ABCD be a rectangle and P be any point in its plane. Show that `PA^(2)+PC^(2)=PB^(2)+PD^(2)` .

If P be any point in the plane of square ABCD, prove that PA^(2)+PC^(2)=PB^(2)+PD^(2)

ABCD is a quadrilateral and O is point in its plane. Show that if vec OA+ vec OB+ vec OC+ vec OD= vec 0 , then O is the point of the interection of the lines joining the mid-points of the opposite sides of ABCD.

Let a vertical tower A B have its end A on the level ground. Let C be the mid point of A B and P be a point on the ground such that A P=2A Bdot If /_B P C=beta, then tanbeta is equal to : (1) 2/9 (2) 4/9 (3) 6/7 (4) 1/4

Let O be the vertex and Q be any point on the parabola, x^2=""8y . It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the question: Let PA=4 , PB=3 cm and CD is diameter of the circle having the length 8 cm. If PC gt PD , then (PC)/(PD) is equal to

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the questions If log_(PA) x=2 , log_(PB)x=3, log_(x) PC=4 , then log_(PD) x is equal to

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the questions If PA=| cos theta + sin theta | and PB=| cos theta - sin theta | , then maximum value of (PC)(PD) , is equal to

If A and B are the points (3, 4, 5) and (-1, 3,-7) respectively then theset of points Psuch that PA ^(2) + PB ^(2) = K ^(2), where K is a constant lie on a proper sphere if:

Let P (n) denote the statement : “ 2^n gen ! ". Show that P(1), P(2) and P(3) are true but P(4) is not true.

ABCD is a parallelogram and P the intersection of the diagonals, O is any point . Show that vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OP) .