Consider the following figure:

Compare the area of the triangle with the area of the sector to prove

Further, prove,

* Proof. * Assume the radius is . For we have the triangle has base length and height the area is

The area of the circular sector is

Since the area of the triangle is less than the area of the sector we have,

Then, since we have for

for

, but since the in the specified range we get , as a result, it doesn't justify . Of course, with its very easy to solve.

Hi, thanks! Yes, that was definitely incorrect. I put up a fix now, and also corrected the typo in the diagram that had the origin labelled with $P$.