Stay ahead of learning milestones! Enroll in a class over the summer!

G
Topic
First Poster
Last Poster
A Segment Bisection Problem
buratinogigle   3
N 10 minutes ago by AGCN
Source: VN Math Olympiad For High School Students P9 - 2025
In triangle $ABC$, let the incircle $\omega$ touch sides $BC, CA, AB$ at $D, E, F$, respectively. Let $P$ lie on the line through $D$ perpendicular to $BC$. Let $Q, R$ be the intersections of $PC, PB$ with $EF$, respectively. Let $K, L$ be the projections of $R, Q$ onto line $BC$. Let $M, N$ be the second intersections of $DQ, DR$ with the incircle $\omega$. Let $S$ be the intersection of $KM$ and $LN$. Prove that the line $DS$ bisects segment $QR$.
3 replies
buratinogigle
Today at 1:36 AM
AGCN
10 minutes ago
No more topics!
Bashing??
John_Mgr   2
N Apr 4, 2025 by GreekIdiot
I have learned little about what bashing mean as i am planning to start geo, feels like its less effort required and doesnt need much knowledge about the synthetic solutions?
what do you guys recommend ? also state the major difference of them... especially of bashing pros and cons..
2 replies
John_Mgr
Apr 4, 2025
GreekIdiot
Apr 4, 2025
Bashing??
G H J
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
John_Mgr
62 posts
#1
Y by
I have learned little about what bashing mean as i am planning to start geo, feels like its less effort required and doesnt need much knowledge about the synthetic solutions?
what do you guys recommend ? also state the major difference of them... especially of bashing pros and cons..
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
AshAuktober
987 posts
#2
Y by
I'd suggest learn normal geometry first , while the point you've made is correct, that's precisely why competition problems are often hard to bash without previous Euclidean observations.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
GreekIdiot
167 posts
#3
Y by
I ll talk about complex bash cause I have never used barycentric coordinates. Usually circles are hard to compute unless its the unit circle so avoid using them when a lot of them are involved. You still need to be able to translate algebraically geometric properties (like $g=\dfrac {a+b+c}{3}$) and you also need to be quite good at algebra. You should start with basic euclidean though and perhaps learn inversion first before trying bashing, you will build the fundamentals you need that way.
Z K Y
N Quick Reply
G
H
=
a