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. 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

let ABC be a right angled triangle at C. If the inscribed circle touches the side AB at D and (AD) (BD)=11, then find the area of triangle ABC. .

let ABC be a right angled triangle at C. If the inscribed circle touches the side AB at D and (AD) (BD)=11, then find the area of triangle ABC. .

A circle passes through three points A, B and C with the line segment AC as its diameter. A line passing through A intersects the chord BC at a point D inside the circle.If angles DAB and CAB are alpha and beta respectively and the distance between the point A and the mid-point of the line segment DC is d, prove that the area of the circle is (pid^2cos^2a)/(cos^2alpha+cos^2beta+2cosalphacosbetacos(beta-alpha)

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.

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

The slope of a median, drawn from the vertex A of the triangle ABC is -2. The co-ordinates of vertices B and C are respectively (-1, 3) and (3, 5). If the area of the triangle be 5 square units, then possible distance of vertex A from the origin is/are.

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)

In the figure, ABCD is a rectangle and E is a point on the side AB. If AB = 10 and AD = 5 what is the area of the shaded region in the figure?

In Fig. 2, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB=29 cm, AD-23 cm, /_B=90° and DS = 5 cm, then the radius of the circle (in cm)