Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle. Also `angleA + angleC = 180^@` , then prove that the vertex D also lie on the same circle.

A quadrilateral ABCD is drawn to circumscribe a circle as shown. Prove that AB+CD=AD +BC.

If a quadrilateral ABCD, the bisector of angleC angleD intersect at O. Prove that angleCOD=(1)/(2)(angleA+angleB)

A quadrilateral ABCD is drawn to circumscribe a circle (see Figure).Prove that AB+CD=AD+BC.

Let A(3,2), B(4, 1),C(3,1), and D(2, 4) be the vertices of a quadrilateral ABCD. Find the area of the quadrilateral formed by joining the midpoints of the sides of the quadrilateral ABCD.

Four point charges +2nC,-3nC,+4nC,-5nC are placed at the vertices A,B,C,D of a square ABCD of side 0.2 m respectively. Calculate the electric field intensity at a point of intersection of the diagonals.

Find the area of the quadrilateral ABCD whose vertices are A(1, 1), B(7,-3), C(12, 2), and D(7, 21).

In the given figure, A, B and C are three points on a circle with centre O such that angle BOC = 30^(@) and angle AOB = 60^(@) . If D is a point on the circle other than the arc ABC, find angle ADC .

ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6. If A lies between the parallel lines at a distance 4 from one of them, then the length of a side of the equilateral triangle is :