I have two similar problems:
1) Draw a circle of radius r. Now circumscribe an equilateral triangle about the circle and then circumscribe another circle about the triangle and then circumscribe a square about that circle and continue indefinitely alternating circle and increasing the sides of a regular polygon. Find the relationship so that you can calculate the radius of the 5th circle, 10th circle, 20th circle etc.
2) Use regular polygons in the form of 2^2n for n = 1,2,... having a radius of r. Circumscribe the regular polygons running through n. There is a relationship between the area of the next polygon and the previous, find that formula.
I've worked quite a bit on these but I don't feel I am getting the answer that is expected. Help please?
1) Draw a circle of radius r. Now circumscribe an equilateral triangle about the circle and then circumscribe another circle about the triangle and then circumscribe a square about that circle and continue indefinitely alternating circle and increasing the sides of a regular polygon. Find the relationship so that you can calculate the radius of the 5th circle, 10th circle, 20th circle etc.
2) Use regular polygons in the form of 2^2n for n = 1,2,... having a radius of r. Circumscribe the regular polygons running through n. There is a relationship between the area of the next polygon and the previous, find that formula.
I've worked quite a bit on these but I don't feel I am getting the answer that is expected. Help please?