Question 1014341
.
Find the perimeter of square which is inscribed in a circle which is also inscribed in another square whose diagonal is 20cm.
---------------------------------------------------------


<pre>
Let us start with the square whose diagonal is 20 cm.

Its side measure is {{{20/sqrt(2)}}}.

I will not explain it. It is clear without explanations, isn't it?


Then the diameter of the circle inscribed into this square is {{{20/sqrt(2)}}} cm. Correct ?


Now consider the square inscribed to the circle whose diameter is {{{20/sqrt(2)}}} cm.

The diagonal of this square is equal to the diameter {{{20/sqrt(2)}}} cm.

Hence, the side of this square is {{{(20/sqrt(2))*(sqrt(2)/2)}}} cm = 10 cm.
</pre>