-
thank you for teaching me the humpty point
by
ihatemath123, Jun 27, 2024, 2:43 PM
-
ORZZZZZZZZZZ
by
avisioner, Jun 19, 2024, 12:02 AM
-
He never had motivation to multiply out random polynomials
by
the_mathmagician, Oct 25, 2023, 1:49 AM
-
Getting a part 3 is unlikely... anyways, if it ever gets released, it would be great if you listed some problems where this methods are useful!
by
Alfombra12, Aug 13, 2023, 10:36 AM
-
still waiting for part 3
by
kn07, Jun 14, 2023, 10:55 PM
-
Orz orz
by
aansc1729, Mar 13, 2023, 1:13 PM
-
waiting for part 3 since 1 year
by
anurag27826, Jul 18, 2022, 11:19 AM
-
pro kid moment
by
the_mathmagician, Feb 15, 2022, 2:21 AM
-
Ded blog
by
SPHS1234, Jan 31, 2022, 7:43 AM
-
orzity orz orz
by
tigerzhang, Oct 15, 2021, 10:08 PM
-
congrats on IMO gold medal!
by
mathlearner2357, Jul 25, 2021, 5:04 AM
-
orzorzorz
by
PEKKA, Jul 21, 2021, 3:55 PM
-
Wow this is awesome!!
Waiting for part3
by
lneis1, Jun 24, 2021, 5:42 PM
-
Part 3 hype
by
NJOY, Jun 15, 2021, 9:29 AM
-
Ooh niceee! Waiting for part 3!
by
L567, Jun 14, 2021, 4:43 AM
-
Something on FE's please
by
Aryan-23, Feb 26, 2019, 5:33 PM
-
Post!!!!!!
by
ELMOliveslong, Feb 22, 2019, 7:55 PM
-
Really amazing!! In fact you also have the skills of presenting things neatly!! waiting for more blog posts!!
by
AlastorMoody, Jan 12, 2019, 7:40 AM
-
A good topic
by
ahwawm, Dec 20, 2018, 3:22 PM
-
Nice post!
by
Rmo, Dec 20, 2018, 2:17 PM
-
Great blog!!
by
AhirGauss, Dec 19, 2018, 2:56 PM
-
@below He must have been busy these days. Have patience, boys. Legends are not made in
one daymere two months, after all.
by
hansu, Dec 12, 2018, 6:52 PM
-
Nice blog! Please add NT
by
Wizard_32, Nov 26, 2018, 12:47 PM
-
No.. this blog cannot die....
by
enthusiast101, Nov 19, 2018, 1:14 PM
-
Nice blog!
by
niyu, Nov 8, 2018, 5:02 AM
-
An "edge" was better
by
anantmudgal09, Nov 1, 2018, 2:48 PM
-
@rajat1603_ Why do people want to know my "preparation story'??? In this blog most (all) of my posts will be mainly about math
by
p_square, Aug 17, 2018, 5:10 AM
-
*PLEASE* let it be about your preparation story
by
rajat1603_, Aug 17, 2018, 3:57 AM
-
I will post something during the weekend.
by
p_square, Aug 16, 2018, 11:33 AM
by p_square, Sep 10, 2018, 10:21 AM 
-HM point and the inverted ![[asy]
defaultpen(fontsize(9pt));
import math;
import olympiad;
unitsize(30);
pair Z,A,B,C,D,E,F,H,T,P,Q,X,M,N,O,L,Y,R;
A=(6,4); B=(7,0); C=(11,0);
M=(B+C)/2;
D=foot(A,B,C);
E=foot(B,C,A);
F=foot(C,A,B);
H=orthocenter(A,B,C);
dot(H);
X=foot(H,A,M);
P=(A+H)/2;
T=orthocenter(A,P,M);
Q=foot(P,A,M);
O=circumcenter(A,B,C);
L=circumcenter(H,B,C);
N=orthocenter(B,C,X);
Z=foot(M,A,T);
Y = extension(F,E,C,B);
draw(B--A--C--B); draw(C--F, heavygreen); draw(E--H, heavygreen); draw(A--H, heavygreen); draw(A--M, heavygreen); draw(C--H, heavygreen); draw(D--B--F, heavygreen); draw(A--T--Q, red); draw(M--Z, red); draw(A--D, dashed+red); draw(T--X--L--M,blue); draw(L--P, blue); draw(T--P, dashed+blue); draw(T--B, red); draw(F--M--E,dotted+purple); draw(E--F--Y--X--H, orange);
draw(circumcircle(A,B,C),dashed+lightred); draw(circumcircle(H,B,C),blue); draw(circumcircle(L,M,T),blue);
draw(circumcircle(X, H, D),dotted+lightred); draw(circumcircle(X, B, F),dotted+lightred); draw(circumcircle(X, C, E),dotted+lightred); draw(circumcircle(A,X,C),heavycyan); draw(circumcircle(A,X,B),heavycyan); draw(circle(T,4.4),orange); draw(circumcircle(A,E,F),purple); draw(circumcircle(Y,X,B),orange); draw(circumcircle(Y,X,C),orange);
dot("$A$",A, dir(150)); dot("$B$",B,dir(215)); dot("$C$",C, dir(270)); dot("$X$",X,dir(30)); dot("$M$",M,dir(60)); dot("$T$",T,dir(150)); dot("$D$",D,dir(225)); dot("$E$",E,dir(0)); dot("$F$",F,dir(270)); dot("$P$",P,dir(45)); dot("$Q$",Q,dir(45)); dot("$O_A$",L,dir(310)); dot("$H$",H,dir(225)); dot("$Y$",Y,dir(300));
[/asy]](//latex.artofproblemsolving.com/f/e/3/fe3946871f19f4409e3993721cd6ce088a558f59.png)
![[asy]
defaultpen(fontsize(9pt));
import math;
import olympiad;
unitsize(50);
pair A,B,C,M,X,O,x1,x2,x3,E,F,H,x4,x5,x6,x7,D,x8,x9,Y,x10,T,P,Oa,x11,Y;
B=dir(150); X=dir(100); C=dir(30);
O=circumcenter(X,B,C);
A=(-1/((B+C)/2-O))+O;
x1=orthocenter(X,B,C); x2=foot(x1,X,((B+C)/2)); x3 = foot(x2,B,C); M = 2*x3-x2;
x4=foot(A,M,C); E=2*x4-C; x5=foot(A,M,B); F=2*x5-B;
H=extension(F,E,B,C);
x6 = foot(O,M,H); D = 2*x6-M;
x7 = foot(O,X,H); Y = 2*x7 - X;
x10 = foot(X,B,C); Oa = 2*x10 - X;
x8 = foot(X,E,F); P=2*x8-X;
x9 = foot(O,M,P); T=2*x9-M;
x11=foot(O,X,H); Y=2*x11-X;
draw(M--A--B--C--A); draw(E--M--F--H--C); draw(M--H, red); draw(C--A--B,heavygreen); draw(F--E--C--B--F,heavygreen); draw(M--P,purple); draw(B--E,blue); draw(C--F,blue); draw(A--D,blue); draw(X--H,blue);
draw(circumcircle(X,C,B)); draw(circumcircle(E,F,B),heavygreen); draw(circumcircle(A,X,H),red); draw(circumcircle(F,X,C),dotted+heavycyan); draw(circumcircle(E,X,B),dotted+heavycyan); draw(circumcircle(A,X,C),dashed+orange);draw(circumcircle(A,X,B),dashed+orange);
dot("$A$",A,dir(90)); dot("$B$",B,dir(200)); dot("$C$",C,dir(270)); dot("$X$",X,dir(180)); dot("$M$",M,dir(270)); dot("$E$",E,dir(20)); dot("$F$",F,dir(270));dot("$H$",H);dot("$D$",D,dir(330));dot("$T$",T,dir(125)); dot("$P$",P,dir(90)); dot("$O_A$",Oa); dot("$Y$",Y,dir(90));
[/asy]](//latex.artofproblemsolving.com/a/c/6/ac68e9085030db405285b5e724b844266465538b.png)
-HM point and the inverted ![[asy]
defaultpen(fontsize(9pt));
import math;
import olympiad;
unitsize(30);
pair Z,A,B,C,D,E,F,H,T,P,Q,X,M,N,O,L,Y,R;
A=(6,4); B=(7,0); C=(11,0);
M=(B+C)/2;
D=foot(A,B,C);
E=foot(B,C,A);
F=foot(C,A,B);
H=orthocenter(A,B,C);
dot(H);
X=foot(H,A,M);
P=(A+H)/2;
T=orthocenter(A,P,M);
Q=foot(P,A,M);
O=circumcenter(A,B,C);
L=circumcenter(H,B,C);
N=orthocenter(B,C,X);
Z=foot(M,A,T);
Y = extension(F,E,C,B);
draw(B--A--C--B); draw(C--F, heavygreen); draw(E--H, heavygreen); draw(A--H, heavygreen); draw(A--M, heavygreen); draw(C--H, heavygreen); draw(D--B--F, heavygreen); draw(A--T--Q, red); draw(M--Z, red); draw(A--D, dashed+red); draw(T--X--L--M,blue); draw(L--P, blue); draw(T--P, dashed+blue); draw(T--B, red); draw(F--M--E,dotted+purple); draw(E--F--Y--X--H, orange);
draw(circumcircle(A,B,C),dashed+lightred); draw(circumcircle(H,B,C),blue); draw(circumcircle(L,M,T),blue);
draw(circumcircle(X, H, D),dotted+lightred); draw(circumcircle(X, B, F),dotted+lightred); draw(circumcircle(X, C, E),dotted+lightred); draw(circumcircle(A,X,C),heavycyan); draw(circumcircle(A,X,B),heavycyan); draw(circle(T,4.4),orange); draw(circumcircle(A,E,F),purple); draw(circumcircle(Y,X,B),orange); draw(circumcircle(Y,X,C),orange);
dot("$A$",A, dir(150)); dot("$B$",B,dir(215)); dot("$C$",C, dir(270)); dot("$X$",X,dir(30)); dot("$M$",M,dir(60)); dot("$T$",T,dir(150)); dot("$D$",D,dir(225)); dot("$E$",E,dir(0)); dot("$F$",F,dir(270)); dot("$P$",P,dir(45)); dot("$Q$",Q,dir(45)); dot("$O_A$",L,dir(310)); dot("$H$",H,dir(225)); dot("$Y$",Y,dir(300));
[/asy]](http://latex.artofproblemsolving.com/f/e/3/fe3946871f19f4409e3993721cd6ce088a558f59.png)
![[asy]
defaultpen(fontsize(9pt));
import math;
import olympiad;
unitsize(50);
pair A,B,C,M,X,O,x1,x2,x3,E,F,H,x4,x5,x6,x7,D,x8,x9,Y,x10,T,P,Oa,x11,Y;
B=dir(150); X=dir(100); C=dir(30);
O=circumcenter(X,B,C);
A=(-1/((B+C)/2-O))+O;
x1=orthocenter(X,B,C); x2=foot(x1,X,((B+C)/2)); x3 = foot(x2,B,C); M = 2*x3-x2;
x4=foot(A,M,C); E=2*x4-C; x5=foot(A,M,B); F=2*x5-B;
H=extension(F,E,B,C);
x6 = foot(O,M,H); D = 2*x6-M;
x7 = foot(O,X,H); Y = 2*x7 - X;
x10 = foot(X,B,C); Oa = 2*x10 - X;
x8 = foot(X,E,F); P=2*x8-X;
x9 = foot(O,M,P); T=2*x9-M;
x11=foot(O,X,H); Y=2*x11-X;
draw(M--A--B--C--A); draw(E--M--F--H--C); draw(M--H, red); draw(C--A--B,heavygreen); draw(F--E--C--B--F,heavygreen); draw(M--P,purple); draw(B--E,blue); draw(C--F,blue); draw(A--D,blue); draw(X--H,blue);
draw(circumcircle(X,C,B)); draw(circumcircle(E,F,B),heavygreen); draw(circumcircle(A,X,H),red); draw(circumcircle(F,X,C),dotted+heavycyan); draw(circumcircle(E,X,B),dotted+heavycyan); draw(circumcircle(A,X,C),dashed+orange);draw(circumcircle(A,X,B),dashed+orange);
dot("$A$",A,dir(90)); dot("$B$",B,dir(200)); dot("$C$",C,dir(270)); dot("$X$",X,dir(180)); dot("$M$",M,dir(270)); dot("$E$",E,dir(20)); dot("$F$",F,dir(270));dot("$H$",H);dot("$D$",D,dir(330));dot("$T$",T,dir(125)); dot("$P$",P,dir(90)); dot("$O_A$",Oa); dot("$Y$",Y,dir(90));
[/asy]](http://latex.artofproblemsolving.com/a/c/6/ac68e9085030db405285b5e724b844266465538b.png)
June 2021
May 2021