[/quote]
,
,
such that 
is a perfect square? (Here 
denotes the integer part of the real number 
?
be an acute triangle with 
,
be the intouch triangle with 
,
,
,
be the intersecttion of the perpendicular from 
to 
with 
,
.
and 
are concylic
the set 
can be partitioned into 
triples in such a way that the numbers from each triple are the lengths of the sides of some obtuse triangle.
,
,
.
and that 
.
and 
be the midpoints of sides 
,
and 
be the feet of the altitudes from 
and 
in 
,
be the intersection of line 
with the tangent line to 
.
be the intersection point, other than 
.
be the intersection of lines 
and 
.
with centre 
passes through 
respectively. Let 
,
is equidistant from 
is a cyclic quadrilateral inscribed in a circle of radius one unit. If 
,
,
,
,
satisfy 
and 
.
of 
such that 
.
and 
)
Prove that if lines 
are similar.
such that 
, where 
are non-negative reals such that 
.
.
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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
