geometry problem

Shame on me I made a boo-boo but I'm not the only one.

ok jugoslav,

I will mark just one of your errors

DB = sqrt(2 * R)             sqrt(2 * R2)   wrong

 \(DB=\sqrt{R^2+R^2}\\ DB=\sqrt{2R^2}\\ DB=\sqrt2 * \sqrt{R^2}\\ DB=\sqrt{2} *R\)

Your answer does not give a ratio at all. We already know that the ratio is r:R    that is given in the question.

Yours does not simplify to that so it is not correct.

PLUS the whole point is to put R in terms of    r  

Note: it is really good that you are questioning my solution.  

That shows everyone here that you are actively learning. 

Your answer is                r : R

                                       1 : 3 - 2√2               ( 1 : -0.17157287525381 )

The correct answer is:      1 : 3 + 2√2         or       1 : 5.828427124746190666

Maybe so, I already said my answer needed to be checked for stupid errors.

Everyone can see that your second post answer #3, which was completely wrong,  has been edited in the past half hour, (after I posted mine.)

Stop trying to be so dishonest.

\(\displaystyle r = (3-2\sqrt{2})R.\)

 If

 \(\displaystyle r = (3+2\sqrt{2})R\)

then r would be greater than R which is nonsense.

Yes that is true.

All answers here must be checked for careless errors.