prove that![$\frac{a}{b} + \sqrt {\frac{b}{c}} + \sqrt[3]{{\frac{c}{a}}} > \frac{5}{2}$](http://latex.artofproblemsolving.com/6/a/6/6a657cb647e279b0745e3189c3f9d54aa25bf976.png)
,
be an arbitrary point on the circumcircle of triangle 
and that line 
is not parallel to line 
be the point on the circumcircle of triangle 
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.
with 
,
intersects the extension of 
at point 
.
is the midpoint of 
,
intersects the circumcircle of 
.
.
Y by Adventure10
Let 
be an isosceles acute triangle (
) with 
and 
be its circumcircle with center 
. A circle 
with its center on 
passes through the points 
and and intersects the circle at a point 
. Prove that 
and 
intersect on and 
.
(M. Rozhkova, Kyiv)
be an isosceles acute triangle (
) with 
and 
be its circumcircle with center 
. A circle 
with its center on 
passes through the points 
and and intersects the circle at a point 
. Prove that 
and 
intersect on and 
.(M. Rozhkova, Kyiv)
This post has been edited 1 time. Last edited by parmenides51, Jan 10, 2020, 10:52 AM
