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

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

Quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC .

Prove that A(BC)=(AB)C

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are lengths 6 cm and 8 cm respectively. Find the sides AB and AC.

In the adjoining figure, quadrilateral ABCD is circumscribed. If the radius of the incircle with centre O is 10 cm and AD is perpendicular to DC, find x.

In the figure, an isosceles triangle ABC with AB=AC circumscribes a circle. Prove that the point of contact P bisects the base BC.

If 4 sides of a quadrilateral ABCD are tangents to a circle, then

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.

In the given figure AB = 8 cm, M is the mid-point of AB. Semi-circles are drawn on Ab with AM and MB as a diameters. A circle with centre 'O' touches all three semi-circles as shown. Prove that radius of this circle is (1)/(6) AB.