 Hello friends, welcome to the session. I am Alka. Let's discuss the given question a vcd is a quadrilateral is a v plus bc plus cd plus da less than twice of a c plus bd Here is a figure a bcd which is a quadrilateral and a c and bd are the diagonals which are intersecting at a point o Now let us consider triangle a o b in Triangle a o o a o b is greater than a b This is our first equation Here we have followed the property that the sum of the length of any two sides of a triangle is greater than the length of the third side now again in triangle b o c is greater than bc This is our second equation Again in triangle C o d o c Plus od is greater than dc This is our third equation and in triangle o a is greater than this is our fourth equation All these four equations are based on the same property That the sum of the length of two sides of a triangle is greater than the length of the third side on adding we get o a plus o b plus o b Plus o c Plus o c Plus o d Plus o d plus o a is greater than a b plus bc Plus dc Plus plus twice of o a Plus twice of o b Plus twice of o c Plus twice of o d is greater than a b Plus bc Plus c d Plus this implies now we all know that o a Plus o c Equal to ac as we can see from the figure that o a plus o c is equal to a c and O b plus o d equal to b d so O a plus o c equal to ac and O b Plus o d equal to vd this implies We take two common and o a Plus o c and again two common from o b and O d is greater than a b plus b c Plus c d Plus this implies now as we have seen that o a plus o c is equal to ac So we'll write twice of ac plus as We have already seen that o a plus sorry o b plus o d is equal to b d So we'll write twice of b d is greater than a b Plus b c Plus c d this implies On taking two common we get ac Plus b d is greater than a b plus b c Plus c d Plus this implies Plus b c Plus c d Plus d a is less than twice of ac plus b d Therefore we can say that he is a b plus b c plus c d plus d a is less than twice of ac plus B d so hope you understood the solution and enjoyed the session keep smiling and take care