Let A B C D be a quadrilateral in which A B is parallel to C D , A B is perpendicular to A D and A B = 3 C D . The area of the quadrilateral A B C D is 4 sq. units. The diameter (in units) of a circle touching all the sides of the quadrilateral is

Step-by-step solution

From the diagram, Area of the trapezium A B C D = 1 2 a + 3 a 2 r = 4 sq. units ⇒ a r = 1 Equation of B C is y = - r 2 x - 3 r y + r 2 x - 3 r = 0 ∵ B C is a tangent to the circle ⇒ r + r 3 - 3 r 1 + r 4 = r ⇒ r 4 + 4 - 4 r 2 = 1 + r 4 ⇒ r = 3 2 units