and 
,
.
and 
on 
and 
are on the same side of 
be midpoint of segment 
be midpoint of segment 
be intersection of 
with 
and 
that verify the following equation for all 
:
be positive real integer such that 
Prove that
such that 
and 
that satisfy the equation 
.
be a circle, and let a line 
intersect 
Circles 
and 
are internally tangent to 
and 
respectively, and both are tangent to 
Similarly, circles 
and 
are externally tangent to 
and 
respectively.
the segment 
has a length of 
and 
find the length of segment 
and 
Prove that
.
Prove that
and 
Prove that
,
,
is not greater than 
.
Y by Mango247, Mango247
Let 
and 
be the feet of the altitudes of a triangle 
drawn from angles 
and 
, respectively. Let 
and 
be the feet of the perpendiculars from and on the straight line 
. The straight lines 
and 
intersect at a point 
. Prove that 
.
and 
be the feet of the altitudes of a triangle 
drawn from angles 
and 
, respectively. Let 
and 
be the feet of the perpendiculars from and on the straight line 
. The straight lines 
and 
intersect at a point 
. Prove that 
.This post has been edited 4 times. Last edited by parmenides51, May 9, 2021, 10:28 AM
Reason: typo, corrected according to #2
Reason: typo, corrected according to #2
and 
are parallel lines. They don't intersect. It should be "The straight lines 
