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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?
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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?
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zephyrcrush78, Jun 15, 2016, 5:24 PM
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why are we counting shouts
contrib pls
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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, Sep 25, 2016, 6:08 PM 
and 
and a common tangent intersects the circles at 
and 
Let the tangents at 
to the circumcircle of triangle 
intersect at 
and let 
be the reflection of 
across the line 
Prove that the points 
are collinear.
and 
and a common tangent intersects the circles at 
and 
Let the tangents at 
to the circumcircle of triangle 
intersect at 
and let 
be the reflection of 
across the line 
Prove that the points 
are collinear.![[asy]
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draw((2.5981849298984625,4.836778227018128)--(-0.3393580015857452,-3.4399165800969693));
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draw((2.5981849298984625,4.836778227018128)--(2.613182939516327,-3.064403826957021));
draw((-0.3393580015857452,-3.4399165800969693)--(5.565723812485446,-2.68889108248242));
/* dots and labels */
dot((-0.96,1.44),dotstyle);
dot((5.039151187356054,1.4513875780348235),dotstyle);
dot((2.5981849298984625,4.836778227018128),dotstyle);
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label("$B$", (3.1969326653957753,-1.994190553540274), NE * labelscalefactor);
dot((-0.3393580015857452,-3.4399165800969693),linewidth(3.pt) + dotstyle);
label("$P$", (-0.6416437414463894,-4.064434008915822), NE * labelscalefactor);
dot((5.565723812485446,-2.68889108248242),linewidth(3.pt) + dotstyle);
label("$Q$", (5.6337817326607444,-3.223397605169506), NE * labelscalefactor);
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label("$S$", (2.8950221614868408,-6.242502644258847), NE * labelscalefactor);
dot((2.891767264032904,-4.150401612543012),linewidth(3.pt) + dotstyle);
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dot((2.613182939516327,-3.064403826957021),linewidth(3.pt) + dotstyle);
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clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](http://latex.artofproblemsolving.com/a/8/0/a80741dc5505597182f8338bac8bd65195278f47.png)
is cyclic.
is the A-symmedian of 
To show 
be the intersection of 
with 
we have that 
(since 
and 
We finish with an angle chase: 
as desired.
so 
.
be the midpoint of 
,
be the feet of the interir and exterior angle bisectors of 
on 
are collinear.
M
(
\
A
May 2017
April 2017