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.
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 an isosceles triangle with 
Let 
be a point on the circumcircle of 
Let 
intersect the extension of 
at 
Let 
be the midpoint of segment 
and let 
be the intersection of 
and 
Let the extension of 
intersect 
and the circumcircle of 
and 
respectively. Given that 
and 
compute the length of 
.
be a subset of 
such that no sum of three distinct elements of 
.
.
that satisfy the equation 
.
be a circle, and let a line 
intersect 
and 
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
Y by HWenslawski
In an equilateral triangle 
, whose side is 
, the line perpendicular to 
is drawn through the point 
, the line perpendicular to 
through point 
and the line perpendicular to 
through point 
. These three lines determine another triangle. Calculate the perimeter of this triangle
, whose side is 
, the line perpendicular to 
is drawn through the point 
, the line perpendicular to 
through point 
and the line perpendicular to 
through point 
. These three lines determine another triangle. Calculate the perimeter of this triangleThis post has been edited 2 times. Last edited by parmenides51, Dec 22, 2022, 12:43 AM
.
.
.
triangles (with side lengths of 
)
;
.
