[/quote]
,
and 
be positive real numbers such that 
.
When equality holds?
such that: 
và 
.
is the circumcircle of 
wwith diameter 
.
and 
intersect at 
. The line perpendicular to 
at point 
intersects the extension of 
at point 
.
at length 
.
, find the measure of 
.
.
set of numbers:
,
i
,
,
,
are given. For each 
,
,![\[ d_{i} = \max \{ a_{j}\mid 1 \leq j \leq i \} - \min \{ a_{j}\mid i \leq j \leq n \}
\]](http://latex.artofproblemsolving.com/6/4/f/64f48f259b0d44340c5162f704420635d79404a8.png)
.
,![\[ \max \{ |x_{i} - a_{i}| \mid 1 \leq i \leq n \}\geq \frac {d}{2}. \quad \quad (*)
\]](http://latex.artofproblemsolving.com/1/9/9/19950d29994fe166d1ce80d193e79ec24de8bda4.png)
be a positive integer which is not a perfect square, and consider the equation ![\[k = \frac{x^2-a}{x^2-y^2}.\]](http://latex.artofproblemsolving.com/c/2/2/c223ccbc272d07c19632c5b8883571023e47a395.png)
Let 
for which the equation admits a solution in 
with 
,
.
.
we can find a set 
of 
is 
.
meets line 
on 
such that 
.
intersects 
.
,
at point 
.
is tangent to 
.
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This post has been edited 19 times. Last edited by jwelsh, Mar 21, 2020, 5:28 PM
Reason: update
Reason: update
