and 
,
.
.
and 
on 
and 
are on the same side of 
be midpoint of segment 
be midpoint of segment 
be intersection of 
with 
and 
that verify the following equation for all 
:
be positive real integer such that 
Prove that
such that 
and 
that satisfy the equation 
.
be a circle, and let a line 
intersect 
Circles 
and 
are internally tangent to 
and 
respectively, and both are tangent to 
Similarly, circles 
and 
are externally tangent to 
and 
respectively.
the segment 
has a length of 
and 
find the length of segment 
and 
Prove that
.
Prove that
and 
Prove that
,
,
is not greater than 
.
Y by Adventure10, Mango247
We are given a line 
with four successive points 
, 
, 
, 
, reading from left to right. Describe a straightedge and compass construction yielding a square 
such that lies on the line 
, on the line 
, on the line 
and on the line 
.
with four successive points 
, 
, 
, 
, reading from left to right. Describe a straightedge and compass construction yielding a square 
such that lies on the line 
, on the line 
, on the line 
and on the line 
.
with diameters 
are on 
Perpendicular bisectors 
of 
cut 
such that 
are on one side of the line 
on the other side. 
are diagonals of the square 
cuts 
again at 
and 
cuts 
again at 
Reflections 
of 
in 
which is reflection of 
