Entering APMOde

by shiningsunnyday, Oct 5, 2016, 1:05 PM

2013 APMO P5 wrote:
Let $ABCD$ be a quadrilateral inscribed in a circle $\omega$, and let $P$ be a point on the extension of $AC$ such that $PB$ and $PD$ are tangent to $\omega$. The tangent at $C$ intersects $PD$ at $Q$ and the line $AD$ at $R$. Let $E$ be the second point of intersection between $AQ$ and $\omega$. Prove that $B$, $E$, $R$ are collinear.
Solution
Tidbit
Tidbit 2
This post has been edited 4 times. Last edited by shiningsunnyday, Oct 12, 2016, 1:27 PM

Comment

4 Comments

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Good luck with the Yale guy! I bet you'll be fine. :)

Rip
This post has been edited 1 time. Last edited by shiningsunnyday, Oct 6, 2016, 5:01 AM

by JunaBug13, Oct 5, 2016, 5:38 PM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Any good sources for learning projective? :maybe: darn should have taken that course at MP

Er you can't learn proj without Ceva, Menelaus, proficiency using ratio lemma, so go learn those first (which along with good synthetic stuff is covered in 106 or geo 2 at AMSP) so go do that first. Then to learn proj get EGMO (though naturally proj comes after a good ton of synthetic configs) or go take Geo 3 then get Lemmas. ...or work through a random handout online.
This post has been edited 1 time. Last edited by shiningsunnyday, Oct 6, 2016, 4:59 AM

by skipiano, Oct 5, 2016, 10:30 PM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
"apmode" was pretty good

:laugh:
This post has been edited 1 time. Last edited by shiningsunnyday, Oct 6, 2016, 5:00 AM

by MathStudent2002, Oct 5, 2016, 11:33 PM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
How did Yale go? Hope it went well. :)

Rip
This post has been edited 1 time. Last edited by shiningsunnyday, Oct 9, 2016, 11:46 AM

by zephyrcrush78, Oct 9, 2016, 6:10 AM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

avatar

shiningsunnyday
Archives
- May 2017
Shouts
Submit
  • this guy is an absolute legend. much love wherever you are Michael

    by LeonidasTheConquerer, Aug 5, 2024, 9:37 PM

  • amazing blog

    by anurag27826, Jun 17, 2023, 7:20 AM

  • hi i randomly found this

    by purplepenguin2, Mar 1, 2023, 8:43 AM

  • can i be a contributor please?

    by cinnamon_e, Mar 10, 2022, 6:58 PM

  • 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. $ \

    by ARay10, Aug 25, 2020, 5:55 PM

  • Nice blog! :)

    by User526797, Jan 12, 2020, 4:48 PM

  • oh my gosh it's been so longggggg.... contrib? what does that mean?

    by adiarasel, Dec 1, 2019, 8:31 PM

  • 2019 post

    by piphi, Aug 10, 2019, 6:32 AM

  • hi contrib please

    by Emathmaster, Dec 27, 2018, 5:38 PM

  • hihihihihi contrib plzzzzz

    by haha0201, Aug 20, 2018, 3:58 PM

  • contrib please

    by Max0815, Aug 1, 2018, 12:35 AM

  • contrib /charmander

    by mathmaster2000, Apr 16, 2017, 4:59 PM

  • for contrib

    by SomethingNeutral, Mar 30, 2017, 7:57 PM

270 shouts
Tags
About Owner
  • Posts: 1350
  • Joined: Dec 19, 2014
Blog Stats
  • Blog created: Jun 11, 2016
  • Total entries: 193
  • Total visits: 30957
  • Total comments: 579
Search Blog
a