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this guy is an absolute legend. much love wherever you are Michael
by
LeonidasTheConquerer, Aug 5, 2024, 9:37 PM
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amazing blog
by
anurag27826, Jun 17, 2023, 7:20 AM
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hi i randomly found this
by
purplepenguin2, Mar 1, 2023, 8:43 AM
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can i be a contributor please?
by
cinnamon_e, Mar 10, 2022, 6:58 PM
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orzorzorzorzorzorozo
by
samrocksnature, Jul 16, 2021, 8:25 PM
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2021 post
by
the_mathmagician, May 5, 2021, 3:28 PM
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Let
be an equilateral triangle of side length 
. Let 
be the point such that 
is the midpoint of 
, and let 
be the incenter of triangle 
. Let 
be the point on line 
such that 
and 
are perpendicular. $ \
by
ARay10, Aug 25, 2020, 5:55 PM
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Nice blog!
by
User526797, Jan 12, 2020, 4:48 PM
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oh my gosh it's been so longggggg.... contrib? what does that mean?
by
adiarasel, Dec 1, 2019, 8:31 PM
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2019 post
by
piphi, Aug 10, 2019, 6:32 AM
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hi contrib please
by
Emathmaster, Dec 27, 2018, 5:38 PM
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hihihihihi contrib plzzzzz
by
haha0201, Aug 20, 2018, 3:58 PM
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contrib please
by
Max0815, Aug 1, 2018, 12:35 AM
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contrib /charmander
by
mathmaster2000, Apr 16, 2017, 4:59 PM
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for contrib
by
SomethingNeutral, Mar 30, 2017, 7:57 PM
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all contrib requests added I usually get to posting every night after running on the treadmill and showering, posting my favorite problem(s) I did during the day.
by
shiningsunnyday, Jun 16, 2016, 4:37 AM
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Since problems is plural, he might post multiple problems through different posts in one day...
by
zephyrcrush78, Jun 15, 2016, 8:37 PM
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hi can i have contrib?
by
wu2481632, Jun 15, 2016, 8:36 PM
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Hello it is called problems of the DAY
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Temp456, Jun 15, 2016, 8:17 PM
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10th shout lol
How often will this blog be updated?
by
zephyrcrush78, Jun 15, 2016, 5:24 PM
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why are we counting shouts
contrib pls
by
MathAwesome123, Jun 15, 2016, 2:55 PM
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eighth shout
contrib pls
by
skipiano, Jun 15, 2016, 2:21 PM
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seventh shout
Can I be contrib?
Though probably not because it's not like I'll post anything anyways :/ :/
by
zephyrcrush78, Jun 15, 2016, 1:20 AM
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sixth shout
new goal: get the shouts that are congruent to 1 mod 5
by
DeathLlama9, Jun 15, 2016, 12:33 AM
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fifth shout >
by
budu, Jun 14, 2016, 10:04 PM
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4th yay
by
EpicSkills32, Jun 14, 2016, 9:10 PM
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third shout
by
skipiano, Jun 14, 2016, 2:35 PM
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Second shout
by
zephyrcrush78, Jun 14, 2016, 12:06 AM
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omg yesssss
by
DeathLlama9, Jun 13, 2016, 2:19 PM
by shiningsunnyday, Oct 5, 2016, 1:05 PM 
be a quadrilateral inscribed in a circle 
, and let 
be a point on the extension of 
such that 
and 
are tangent to 
intersects 
and the line 
at 
. Let 
be the second point of intersection between 
and 
, 
be a quadrilateral inscribed in a circle 
, and let 
be a point on the extension of 
such that 
and 
are tangent to 
intersects 
and the line 
at 
. Let 
be the second point of intersection between 
and 
, ![[asy]/* DRAGON 0.0.9.6
Homemade Script by v_Enhance. */
import olympiad;
import cse5;
size(11cm);
real lsf=0.8000;
real lisf=2011.0;
defaultpen(fontsize(10pt));
/* Initialize Objects */
pair P = (4.0, -6.0);
pair O = (4.0, 2.0);
pair D = (7.794019966423534, -0.7329512659808339);
path DP = D--P;
pair A = (0.7383826268204343, 5.350442096025524);
pair C = (2)*(foot(O,A,P))-A;
pair B = 2*foot(D,relpoint(O--P,0.5-10/lisf),relpoint(O--P,0.5+10/lisf))-D;
pair T = IntersectionPoint(Line(B,D,lisf),Line(O,midpoint(A--C),lisf));
pair Q = IntersectionPoint(DP,Line(T,C,lisf));
pair Z = IntersectionPoint(Line(A,B,lisf),Line(T,C,lisf));
pair R = IntersectionPoint(Line(A,D,lisf),Line(T,C,lisf));
pair E_prime = (foot(O,A,Q))*(2)-A;
path BD = T--D;
path AP = A--P;
pair K = IntersectionPoint(BD,AP);
/* Draw objects */
draw(DP, rgb(0.6,0.0,0.6));
draw(CirclebyPoint(O,D), rgb(0.8,0.0,0.8) + linewidth(1.2));
draw(B--P, rgb(0.6,0.0,0.6));
draw(BD, rgb(0.8,0.0,1.0) + dashed);
draw(T--A, rgb(1.0,0.6,1.0));
draw(T--R, rgb(1.0,0.6,1.0));
draw(A--R, rgb(1.0,0.6,1.0));
draw(A--Z, rgb(1.0,0.0,0.8));
draw(AP, rgb(0.8,0.0,1.0) + dashed);
draw(B--R, rgb(1.0,0.0,0.8));
draw(A--Q, rgb(0.8,0.0,0.4) + linetype("4 4"));
/* Place dots on each point */
dot(P);
dot(D);
dot(A);
dot(C);
dot(B);
dot(T);
dot(Q);
dot(Z);
dot(R);
dot(E_prime);
dot(K);
/* Label points */
label("$P$", P, lsf * dir(0));
label("$D$", D, lsf * dir(0));
label("$A$", A, lsf * dir(135));
label("$C$", C, lsf * dir(45));
label("$B$", B, lsf * dir(225));
label("$T$", T, lsf * dir(135));
label("$Q$", Q, lsf * dir(-60));
label("$Z$", Z, lsf * dir(-90));
label("$R$", R, lsf * dir(-90));
label("$E'$", E_prime, lsf * dir(70));
label("$K$", K, lsf * dir(45));
[/asy]](http://latex.artofproblemsolving.com/d/a/2/da29698a481a411535910c6836714d2f4fd60fee.png)
is a harmonic quad, 
(where 
is the tangent to 
)
Because 
are tangents, we have 
harmonic. It suffices to show 
is harmonic, which would imply 
We finish by observing 
May 2017
April 2017