have the property that both![\[
\left\lfloor \sqrt{2n - 1} \right\rfloor \quad \text{and} \quad \left\lfloor \sqrt{3n + 2} \right\rfloor
\]](http://latex.artofproblemsolving.com/d/e/c/dec527c4673470e7023d6aed00fac90268bd2fcc.png)
are consecutive perfect squares.
such that
is an integer.
,
be the foot of the altitude from 
be a point in the interior of the segment 
.
be the point on the segment 
such that 
.
be the point on the segment 
such that 
.
be the point of intersection of 
and 
.
.
be a point on segment 
.
be a fixed circle passing through 
be a variable point on 
be the intersection of the tangent to the circumcircle of 
at 
and the tangent to the circumcircle of 
at 
.
Y by Adventure10, Mango247
Given the equilateral triangle 
. It is known that the radius of the inscribed circle is in this triangle is equal to 
. The rectangle 
is such that point 
belongs to its side 
. Find the radius of the circle circumscribed around the rectangle .
. It is known that the radius of the inscribed circle is in this triangle is equal to 
. The rectangle 
is such that point 
belongs to its side 
. Find the radius of the circle circumscribed around the rectangle .This post has been edited 1 time. Last edited by parmenides51, Nov 7, 2022, 9:33 PM
and breadth 
,
.
.
,
.
is 
.
.
has a circumradius of 
