[/quote]
,
is called stylish if the set 
can be partitioned into 
pairs such that the sum of the elements in each pair is a power of 
.
is stylish because the set 
can be partitioned as 
,
,
.
that verify the following equation for all 
:
is a prime number
to the cross product 
reveals that a negative determinant [of 
] corresponds to a matrix which reverses the direction of the cross product of two vectors.[/quote]
and 
,
and 
although its supposed to be a quick comparison.
is a function for which the expression 
for all 
is always a perfect square. Prove that 
for all 
.
such that 
.
be a quadrilateral inscribed in a circle 
,
be a point on the extension of 
such that 
and 
are tangent to 
intersects 
and the line 
at 
.
be the second point of intersection between 
and 
,
be a triangle with incenter 
,
and 
.
and 
the reflections of 
with 
,
be the midpoint of 
and 
are perpendicular.
chance of landing heads when flipped. Krithik is playing a game where he starts with 
point. Every turn, he flips the coin, and if it lands heads, he gains 
points. Find the expected number of turns until Krithik wins.
.
be the feet of the altitudes from 
to 
respectively. Let 
be the midpoint of 
be the circle with diameter 
be the intersection of 
and 
be the intersection of 
be the lines through 
respectively. Let 
and 
.
and 
.
be the line through 
and let 
be the reflection of 
is tangent to 
.
be a function from the Euclidean plane to the real numbers such that 
for any acute triangle 
with circumcenter 
is constant.
be tangent to the side 
.
on 
on 
lies on the circumcircle of triangle 
.
be an isosceles triangle with 
Let 
Let 
intersect the extension of 
at 
Let 
and let 
and 
Let the extension of 
intersect 
and the circumcircle of 
respectively. Given that 
and 
compute the length of 
Y by HWenslawski
Consider the following circle and regular hexagon (six congruent sides) as it is shown in the picture.
The segment
is a side of the hexagon and the diameter of the circle. Let 
and 
the areas of the circle and the hexagon respectively. What is the value of 
?
The segment
is a side of the hexagon and the diameter of the circle. Let 
and 
the areas of the circle and the hexagon respectively. What is the value of 
?This post has been edited 1 time. Last edited by parmenides51, Jul 23, 2021, 2:53 PM
and the area of the hexagon is 
