Since I got tired of sucking at non-geo

by shiningsunnyday, Sep 20, 2016, 7:41 PM

1998 ISL G5 / Lemmas in Oly Geo wrote:
Let $ABC$ be a triangle with orthocenter $H,$ circumcenter $O$ and circumradius $R.$ Let $D, E, F$ be the reflections of the vertices $A, B, C$ across the opposite sides. Prove that they are collinear if and only if $OH=2R.$
Solution

Tidbit
This post has been edited 5 times. Last edited by shiningsunnyday, Oct 6, 2016, 11:41 AM

Comment

4 Comments

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ssd pls add size(250); in front of the last two asy diagrams

bad ssd

need to resize your diagrams

Dude it makes the diagrams even more jumbled up !
This post has been edited 1 time. Last edited by shiningsunnyday, Sep 21, 2016, 1:45 AM

by agbdmrbirdyface, Sep 21, 2016, 12:01 AM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
wait I suck at geo

Get something like 106 or 107 and beast mode it
This post has been edited 1 time. Last edited by shiningsunnyday, Sep 21, 2016, 7:16 AM

by skipiano, Sep 21, 2016, 3:53 AM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
or you could do the other obvious thing. reflections, orthocenter, circumcenter – it screams the $H$ reflecting over the sides theorem. so just reflect the circumcircle over the sides i think

Please show thunk
This post has been edited 1 time. Last edited by shiningsunnyday, Sep 21, 2016, 3:45 PM

by cjquines0, Sep 21, 2016, 3:33 PM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
WAIT YAY JUST REALIZED THIS WAS 1998 G5

by shiningsunnyday, Sep 22, 2016, 2:19 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: 30959
  • Total comments: 579
Search Blog
a