such that 
and 
with another positive integer 
,
is a perfect square. For example, if the number on the blackboard is 
,
,
,
,
.
,
with circumcenter 
and orthocenter 
,
be an arbitrary point on the circumcircle of triangle 
and that line 
is not parallel to line 
.
be the point on the circumcircle of triangle 
is perpendicular to 
be the point on line 
such that 
.
and 
be the points on the circumcircle of triangle 
is a diameter, and 
and 
are parallel. Let 
be the midpoint of 
.
and 
are perpendicular.
and 
are perpendicular.
Y by Loppukilpailija, anantmudgal09, atmchallenge, Gems98, FEcreater, rocketscience, 62861, MathStudent2002, MNJ2357, v_Enhance, MarkBcc168, pieater314159, lminsl, Kayak, tapir1729, SAUDITYA, TacH, rmtf1111, enthusiast101, TLP.39, psi241, Pluto1708, ThE-dArK-lOrD, falantrng, Kagebaka, XbenX, ririri, math_pi_rate, khan.academy, tastymath75025, Pathological, fry8, Mathuzb, YRNG-BCC168, MK4J, cooljoseph, nicolino, Ankoganit, stroller, Aritra12, Adventure10, Mango247
TL;DR: MO 3 and new experimental JMO, can take both, sign-up link, problems posted 19 and 20 March, deadline 8 April. Have fun!
What's New
Twelve new problems. Twelve? Yes, in addition to the MO 3, there will also be an experimental JMO. 6+6-12=0, so the MO 3 and the experimental JMO will be disjoint, meaning that you can take both of them! (read: we hope you take both)
About Us
We are a group of Thai students sharing the hobby of proposing olympiad math problems. Most of us had been in the Thailand TST Camp, and several of us are IMO medalists. Some of our members are @ThE-dArK-lOrD and @TacH, who will be co-hosting the MO 3 with me. We have also just launched our website (still kinda work-in-progress): https://www.infinitydots.org.
For the past two years, we have been publishing our problems in InfinityDots MOs—hence the number 3 this year.
MO 1 (2017): main thread, problems
MO 2 (2018): announcement, main thread, problems
Formal Stuff
- Sign-ups are now open in a separate thread (so we don't flood HSO). If you sign up, (i) we’ll notify you when the contest starts, and (ii) it’ll bump that thread up. There’s also the option to privately sign-up—just PM me.
- Both the MO 3 and the experimental JMO will start (i.e. day 1 problems posted) on 19 March at 10am EDT, day 2 problems will be posted 20 March 10am EDT.
- Window for submitting solutions lasts until 8 April 10pm EDT. Scores will be released around a week after that (but definitely before the USA(J)MO) depending on how fast we can grade and how many people submit. Submissions can be done in two ways: either PM me (@talkon) here on AoPS, or send an email to mo3@infinitydots.org.
FAQs
Q: Is the sign-up list for both the MO 3 and the JMO?
A: Yeah, the same sign-up list is used for both the MO 3 and the JMO. Which one (or two) you will take is your choice. You can take only the MO, only the JMO, or both!
Q: Are there any awards?
A: Sadly, no, but we hope you enjoy the experience of solving our problems.
Q: Anything I can do to help you?
A: We are not accepting any testsolvers or graders publicly, but feel free to help us spread the word.
If you have more questions, feel free to ask in this topic. We hope you enjoy our contest!
This post has been edited 3 times. Last edited by talkon, Mar 8, 2019, 3:21 PM
Reason: update
Reason: update
), please do so by 
are scores for submitted problems.) The total and average score for each problem are also provided.
