Question

the side of the largest size regular hexagon that can be inscribed in a circle of radius 30 mm is​

Answer 1

Side length of the hexagon= 30mm

Logic is very simple. It's a regular hexagon. ie, all the sides of the polygon are equal. It's inscribed in a circle.

If its every vertex is joined with the center of the circle, you will find that central angle,that is 360° is divided into 6 equal parts. So each angle at the center = 60°.

Now radius = 30mm. Which implies that 2 sides of the triangle =30mm. That shows every triangle is isosceles. But one of its angles =60° So other 2 base angles have to be 60° each.

This implies that the triangle is an equilateral triangle. So all the sides of the triangle= 30mm.

=> side of the hexagon= 30mm