ABCD is a rectangle AC is diagonal. Find the nature of `DeltaACD`. Give reasons.

ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB. Prove that (i) ar (ABCD) = ar(ABEF) (ii) ar (ABCD) = AB xx DG

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

ABCD is a rectangular A circle circumscribing the rectangle. The coordinates of A and C are (-3, 4) and (5, 4) respectively. Coordinate of centre of the circle will be -

ABCD is a rectangular A circle circumscribing the rectangle. The coordinates of A and C are (-3, 4) and (5, 4) respectively. Equation of circle will be -

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

Superoxides are paramagnetic in nature. Give reason.

In right angled triangle ABC , /_A is a right angle. AD is perpendicular on the hypotenuse BC . Prove that (DeltaABC)/(DeltaACD)=(BC^(2))/(AC^(2)) .

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

The coordinates of the points A,B,C are (-2,1),(-1,-3) and (3,-2) respectively . Show that , AB =BC and angleABC is a right angle If D is the fourth vertex of the square ABCD , find the coordinates of D and also find the point of intersection of diagonals of ABCD.