[/quote]
,
.
for 
Thus the first few terms are 
,
.
is called frameable if it is possible to draw a regular polygon with 
sides all whose vertices lie on these lines, and no line contains more than one vertex of the polygon.
are frameable.
is not frameable.
is frameable.
,
with integer coefficients such that 
divides 
for every positive integer 
are constructed the squares 
and 
.
.
such that
for all real numbers 
satisfying the equation
?
has circumcenter 
.
and 
intersect at 
,
and 
intersect at 
and 
and 
intersect at 
.
are similar(with vertices in that order), than 
candidates and 
is an odd integer. Each candidate is evaluated by each judge as either pass or fail. Suppose that each pair of judges agrees on at most ![\[{\frac{k}{m}} \geq {\frac{n-1}{2n}}. \]](http://latex.artofproblemsolving.com/3/8/7/387c8824b28f6422306e3c25b34fccb0a841f4cd.png)
be the feet of the altitudes from 
respectively. Let 
be the projections of 
.
.
have the property that 
is a perfect square for infinitely many positive integers 
?
Y by Mango247
Points 
and 
are located on sides 
and 
of square 
respectively so that triangle 
is isosceles right-angled triangle with a right angle at the vertex 
. From point 
draw a straight line parallel to 
, which intersects the segment 
at point 
. In what angle do lines 
and 
intersect?
and 
are located on sides 
and 
of square 
respectively so that triangle 
is isosceles right-angled triangle with a right angle at the vertex 
. From point 
draw a straight line parallel to 
, which intersects the segment 
at point 
. In what angle do lines 
and 
intersect?This post has been edited 2 times. Last edited by parmenides51, Feb 23, 2021, 4:48 PM
is the midpoint of 
,
, and the line parallel to 
lines intersect at 
