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 
Y by Adventure10
In the convex quadrilateral 
on the diagonal 
a point 
is marked. Through point we draw lines 
and 
such that 
and 
. We set 
as the intersection point of 
and 
, 
is the intersection point of the line 
and 
. Prove that the midpoint of the segment 
lies on 
, where 
is the midpoint of 
, 
is the midpoint of 
.
on the diagonal 
a point 
is marked. Through point we draw lines 
and 
such that 
and 
. We set 
as the intersection point of 
and 
, 
is the intersection point of the line 
and 
. Prove that the midpoint of the segment 
lies on 
, where 
is the midpoint of 
, 
is the midpoint of 
.This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 2:33 AM
and 
respectively, such that 
prove that 
and 
,
so 
is sent to 
under the spiral similarity sending 
to 
Since spiral similarities come in pairs, 
share the same spiral center and the original problem and generalization both immediately follow. 
I feel stupid rip
,
