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 circle passing through the vertex C of a rectangle ABCD and touching its sides AB and AD at M and N, respectively. If the distance from C to the line segment MN is equal to 5 units, then find the area of the reactangle ABCD.

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

ABC is a right triangle, right - angled at the vertex A. A circle is drawn to touch the sides AB and AC at points P and Q respectively such that the other end points of the diameters passing through P and Q lie on the side BC. IF AB = 6 units, then the area (in sq. units) of the circular sector which lies inside the triangle is

ABCD is a parallelogram . The circle passing through the vertices. A, B and C intersects CD (or CD produced) at E. Prove that AE=AD .

In rectangle ABCD above, arcs BP and CP are quarter circles with centers at points A and D, respectively. If the area of each quarter circle is pi , what is the area of the shaded region?

Let ABCD be a rectangle such that AB=10 units and BC=8 units. Taking AB and AD as x and y axis respectively, find the coordinates of A, B, C and D.

P is a point inside the triangle ABC. Lines are drawn through P, parallel to the sides of the triangle.The three resulting triangles with the vertex at P have areas 4,9 and 49 sq . units. The area of the triangle ABC is -

A circle touches a rectangle ABCD of side lengths 2a and 2b at M and N on sides AB and AD respectively , it also passes through the point C. If perpendicular distance of the line MN from points C is 6 cm. Then value of ab is ____

Let ABCD be a square of side length 2 units. C_(2) is the fircle through the vertices A, B, C, D and C_(1) is the circle touching all the of the square ABCD. L is a lien through vertex A. A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line L. The locus of the centre of the circle is

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