A quarter-circle (R) is inscribed in a square. A circle (r) is drawn. Find the ratio of r to R.

Guest Sep 25, 2020

#2**+2 **

The diagonal of the square is \(\sqrt{2R^2}\)

You need to check my working for stupid errors.

Melody Sep 26, 2020

#4**+1 **

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.

Melody
Sep 27, 2020

#5**0 **

Your answer is r : R

1 : 3 - 2√2 ( 1 : -0.17157287525381 )

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

jugoslav
Sep 27, 2020

#6**0 **

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.

Melody
Sep 27, 2020