Chasing cute angles

by shiningsunnyday, Apr 9, 2017, 5:32 AM

2017 EGMO P1 wrote:

Let $ABCD$ be a convex quadrilateral with $\angle DAB=\angle BCD=90^{\circ}$ and $\angle ABC> \angle CDA$ . Let $Q$ and $R$ be points on segments $BC$ and $CD$ , respectively, such that line $QR$ intersects lines $AB$ and $AD$ at points $P$ and $S$ , respectively. It is given that $PQ=RS$ .Let the midpoint of $BD$ be $M$ and the midpoint of $QR$ be $N$ .Prove that the points $M,N,A$ and $C$ lie on a circle.

Solution

EGMO

Angle Chasing

Solved

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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
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
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...
by zephyrcrush78, Jun 15, 2016, 8:37 PM
hi can i have contrib?
by wu2481632, Jun 15, 2016, 8:36 PM
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

contrib pls
by MathAwesome123, Jun 15, 2016, 2:55 PM
eighth shout
contrib pls
by skipiano, Jun 15, 2016, 2:21 PM
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
sixth shout

new goal: get the shouts that are congruent to 1 mod 5
by DeathLlama9, Jun 15, 2016, 12:33 AM
fifth shout >
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4th yay
by EpicSkills32, Jun 14, 2016, 9:10 PM
third shout
by skipiano, Jun 14, 2016, 2:35 PM
Second shout
by zephyrcrush78, Jun 14, 2016, 12:06 AM
omg yesssss
by DeathLlama9, Jun 13, 2016, 2:19 PM

270 shouts

Problems of the day

Chasing cute angles

by shiningsunnyday, Apr 9, 2017, 5:32 AM

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