Wooohoooo

by shiningsunnyday, Nov 4, 2016, 10:15 PM

2014 USAJMO 6 wrote:

Let $ABC$ be a triangle with incenter $I$ , incircle $\gamma$ and circumcircle $\Gamma$ . Let $M,N,P$ be the midpoints of sides $\overline{BC}$ , $\overline{CA}$ , $\overline{AB}$ and let $E,F$ be the tangency points of $\gamma$ with $\overline{CA}$ and $\overline{AB}$ , respectively. Let $U,V$ be the intersections of line $EF$ with line $MN$ and line $MP$ , respectively, and let $X$ be the midpoint of arc $BAC$ of $\Gamma$ .

(a) Prove that $I$ lies on ray $CV$ .

(b) Prove that line $XI$ bisects $\overline{UV}$ .

Solution
Tidbit

USAJMO

geometry

Angle Chasing

Cyclic Quadrilaterals

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You could try IRan TST 2009/9 according to V_enhance this problem is a sub problem in that problem. Also don't be scares of that 9

by First, Nov 5, 2016, 1:35 AM

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@First That isn't completely true. I myself have worked through Iran TST 2009/9, and I can say that part (b) is not used at all. On the other hand, part (a) can be put into good use.

by zephyrcrush78, Nov 5, 2016, 1:38 AM

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that iran tst problem is legitimately trivialized through well-known configs tho
seriously

by wu2481632, Nov 5, 2016, 2:01 AM

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this guy is an absolute legend. much love wherever you are Michael
by LeonidasTheConquerer, Aug 5, 2024, 9:37 PM
amazing blog
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hi i randomly found this
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can i be a contributor please?
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orzorzorzorzorzorozo
by samrocksnature, Jul 16, 2021, 8:25 PM
2021 post
by the_mathmagician, May 5, 2021, 3:28 PM
Let $ABC$ be an equilateral triangle of side length $1$ . Let $D$ be the point such that $C$ is the midpoint of $BD$ , and let $I$ be the incenter of triangle $ACD$ . Let $E$ be the point on line $AB$ such that $DE$ and $BI$ are perpendicular. $ \
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Nice blog!
by User526797, Jan 12, 2020, 4:48 PM
oh my gosh it's been so longggggg.... contrib? what does that mean?
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2019 post
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contrib /charmander
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for contrib
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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
Since problems is plural, he might post multiple problems through different posts in one day...
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hi can i have contrib?
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Hello it is called problems of the DAY
by Temp456, Jun 15, 2016, 8:17 PM
10th shout lol
How often will this blog be updated?
by zephyrcrush78, Jun 15, 2016, 5:24 PM
why are we counting shouts

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eighth shout
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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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new goal: get the shouts that are congruent to 1 mod 5
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fifth shout >
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270 shouts

Problems of the day

Wooohoooo

by shiningsunnyday, Nov 4, 2016, 10:15 PM

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