[/quote]
,
,
,
lie on a circle 
.
at 
and 
.
intersect again at 
.
.
and 
.
Equality holds when 
or 
Equality holds when 
intersect its circumcircle 
at 
.
determine a triangle 
,
is relative to 
are concurrent at a point 
and 
.
be a cyclic quadrilateral whose opposite sides are not parallel. Suppose points 
lie in the interiors of segments 
respectively, such that 
Let 
intersect 
at 
,
intersect 
at 
and 
are either parallel or coincide.
and 
.
Where 
such that :
.
be reals such that 
Prove that 
Let 
Prove that 
be a fixed integer. There are 
beads on a circular necklace. You wish to paint the beads using 
colors, such that among any 
consecutive beads every color appears at least once. Find the largest value of 
for which this task is 
possible.
This easy via the binomial theorem for the quantity is just 
,
satisfies 
.
,
.
Y by Mango247, Mango247, Mango247
Circles 
and 
are tangent at a point 
, and lies inside . A chord 
of is tangent to at 
. The line 
meets again at 
. Chords 
and 
of are tangent to . Let 
and 
be the incentres of triangles 
and 
respectively. Prove that 
.
and 
are tangent at a point 
, and lies inside . A chord 
of is tangent to at 
. The line 
meets again at 
. Chords 
and 
of are tangent to . Let 
and 
be the incentres of triangles 
and 
respectively. Prove that 
.This post has been edited 1 time. Last edited by parmenides51, Jan 14, 2021, 8:41 PM
