be a triangle with 
let 
be the circumcircle of 
and let 
be its radius. Point 
such taht 
and point 
is the foot of the perpendicular from 
.
mets 
.
is chosen on line 
such that 
and 
lie on a line in that order. Finally, let 
be a point satisfying 
and 
.
,
has two real roots, so that the one is the square of the other.
,
be all positive integers smaller than 
such that 
for all 
is the largest positive integer that divides both 
.
.
such that: ![\[ x = \sqrt{ x - \frac{1}{x} } + \sqrt{ 1 - \frac{1}{x} } \]](http://latex.artofproblemsolving.com/e/c/f/ecf7fb3c2805290f2cb07b7fdd7c73e1c7a55b99.png)
Y by Adventure10, Mango247
Let 
be a plane and two points 
. For each line in 
through 
, let 
be the foot of the perpendicular from 
to the line. Find the locus 
of .
Denote by
the oblique cone with peak and base . Prove that all planes, either parallel to or perpendicular to 
, intersect by circles.
Consider the two symmetric faces of that intersect by the angles 
and 
respectively. Find a relation between and .
be a plane and two points 
. For each line in 
through 
, let 
be the foot of the perpendicular from 
to the line. Find the locus 
of .Denote by
the oblique cone with peak and base . Prove that all planes, either parallel to or perpendicular to 
, intersect by circles.Consider the two symmetric faces of
that intersect by the angles 
and 
respectively. Find a relation between and .This post has been edited 1 time. Last edited by parmenides51, Aug 22, 2018, 9:34 AM
Reason: better formulation
Reason: better formulation
,
.
of the points 
.
