INTERNATIONAL MATH OLYMPIAD 2023 | Problem 2

In this video, we present a solution to IMO 2023/2.
Check out the other problems from day 1:
Problem 1: • INTERNATIONAL MATH OLY...
Problem 3: • INTERNATIONAL MATH OLY...
00:00 Problem Statement
01:06 Solution
Wiki links to used statements:
- 03:48 calimath.org/wiki/pascals-the...
Check out our website www.calimath.org to find past problems, solutions and other cool stuff.
Solution PDF: calimath.org/pdf/IMO2023-2
branch: geometry
difficulty: 9
Our website: www.calimath.org
Contact us: [e-mail]

[@hungcuang2019]

I think it would be impossible for me to solve this problem until I see this video. What a nice solution!

[@Maths_3.1415]

Neat and clean solution 😊

[@muhamedbabe8924]

Very nice solution 👌👌

[@carryminati-mk7wv]

Nice explanation 😊

[@mohamedleminekhayar3713]

Think you ❤

[@mohamedleminekhayar3713]

Oh bro think you soooooooooo much ❤❤❤

[@thomasneal7126]

I could not have explained any better myself

[@likemath.]

Hay lắm❤❤❤❤

[@digxx]

angle(SCB)=180-angle(SPB) 🙂

[@calimath6701]

We used directed angles modulo 180. This means angle(SCB) =180-angle(BPS)=-angle(BPS)=angle(SPB). The last equality follows, because swapping B and S changes the direction and therefore, the - sign turns to a +. If you want to have a more detailed description, you can have a look on our wiki entry on our website about directed angles. calimath.org/wiki/directed-angles

[@Alexander-oh6ps]

i used a different approach (using only second grade knowledge aka no Pascal) by proving that XZ=XA=XP, then proving that LZX is a right angle, therefore XZ and XP are tangents of (BLD)

[@calimath6701]

Sounds like a cool approach

[@cyborgeatsfood8028]

W solution

[@farmonov_piima]

Hello uzb🇺🇿

[@NoNameAtAll2]

1:55 it should be 180-spb, right?

[@calimath6701]

We use directed angles modulo 180°. So, SPB = 180° + SPB = 180° - BPS are all correct.

[@mohamedleminekhayar3713]

But why tou don’t prove ppzBDY > cone for use the theorem de pascal you need to prouve that

[@calimath6701]

That's what I did in the first three steps. I proved that P, Z, B, D, and Y lie on one circle, which is a cone.

[@mohamedleminekhayar3713]

@@calimath6701 what about pp(tangent) ? Do you prove pp are in the same cone with pzbdy?

[@AdminAdminilka]

l will never be able to solve any İMO problem

[@BigMotion1]

I can't even solve AIME problems...but if we keep learning, we will be able to