Let $$ABCD$$ be a quadrilateral with area $$18$$, with side $$AB$$ parallel to the side $$CD$$ and $$2AB=CD$$. Let $$AD$$ be perpendicular to $$AB$$ and $$CD$$. If a circle is drawn inside the quadrilateral $$ABCD$$ touching all the sides, then its radius is

One angle of an isosceles $$\Delta $$ is $${120^ \circ }$$ and radius of its incircle $$ = \sqrt 3 $$. Then the area of the triangle in sq. units is

In a triangle $$ABC$$, $$a,b,c$$ are the lengths of its sides and $$A,B,C$$ are the angles of triangle $$ABC$$. The correct relation is given by

In an equilateral triangle, $$3$$ coins of radii $$1$$ unit each are kept so that they touch each other and also the sides of the triangle. Area of the triangle is