,
be the angles of a triangle, and let 
,
.
,![\[s(s - a)(s - b)(s -c) \geq 0.\]](http://latex.artofproblemsolving.com/1/3/4/1344a0cbbd4e1aa4bcf6a1e777501c62daff32b3.png)
has 
.
is the foot of the perpendicular from 
.
and 
lie on sides 
,
and ![\[
\angle CHS - \angle CSB = 90^{\circ}, \quad \angle THC - \angle DTC = 90^{\circ}. \]](http://latex.artofproblemsolving.com/f/8/c/f8c35912c531eb2dae8f62b74666b7757d2b9ba3.png)
Prove that line 
.
of positive integers that satisfy
Y by Resolut1on07, Rounak_iitr, GeoKing, pomodor_ap, Kizaruno, ehuseyinyigit
Given 
. Let the perpendicular line from 
to 
meets 
at points 
, respectively, and the foot from 
to 
is 
. 
intersects line 
at 
, 
intersects line at 
, and lines 
intersect at 
.
Prove that
is tangent to 
.
. Let the perpendicular line from 
to 
meets 
at points 
, respectively, and the foot from 
to 
is 
. 
intersects line 
at 
, 
intersects line at 
, and lines 
intersect at 
.Prove that
is tangent to 
.Attachments:
This post has been edited 1 time. Last edited by Itoz, Apr 18, 2025, 11:53 AM
to 
,
and 
.
and 
meet at a point 
.
is the tangent point. The rest is easy
