Question

a regular hexagon is inscribed in a circle of radius 4 cms. if tangents are drawn to all the vertices of hexagon,find the area enclosed by tangent lines.

Answer 1

Notice that the new hexagon--the one drawn with the tangent lines, consists of six equilateral triangles with a vertical height equal to the radius of the circle.

Now use a trig function of 60 degrees to find the length of the base of the triangle.