satisfying 
and orthocenter 
,
and that line 
is not parallel to line 
.
is perpendicular to 
be the point on line 
such that 
.
and 
be the points on the circumcircle of triangle 
is a diameter, and 
and 
are parallel. Let 
be the midpoint of 
.
and 
are perpendicular.
and 
are perpendicular.
be positive integers and 
be an odd prime such that:![\[
a^p \equiv 1 \pmod{p^n}.
\]](http://latex.artofproblemsolving.com/3/4/8/34815b8211ded2f37b0653525dc4b436356e6eee.png)
Prove that:![\[
a \equiv 1 \pmod{p^{n-1}}.
\]](http://latex.artofproblemsolving.com/0/7/a/07a4ed2ab3c94f41028080f7789cfb6e2973955c.png)
be a cyclic quadrilateral. A circle centered at 
and 
)
Prove that if lines 
are concurrent, then triangle 
are similar.
Y by
Let 
be a right triangle with 
. Points 
and 
, located on the legs 
and 
respectively, are the legs of the inner bisectors taken from the vertices 
and 
, respectively. Let 
be the center of the circle inscribed in the triangle . If 
, find the area of the triangle 
(in terms of parameter 
)
be a right triangle with 
. Points 
and 
, located on the legs 
and 
respectively, are the legs of the inner bisectors taken from the vertices 
and 
, respectively. Let 
be the center of the circle inscribed in the triangle . If 
, find the area of the triangle 
(in terms of parameter 
)This post has been edited 3 times. Last edited by parmenides51, Jul 11, 2020, 5:22 PM
