## Search found 244 matches

Sat May 11, 2013 3:20 pm
Forum: Geometry
Topic: Angle Equity
Replies: 1
Views: 1542

### Re: Angle Equity

Note that ,
$A,Q,P,D$ are harmonic .
Now pencil $C(A,Q,P,D)$ imply , $F,Q,E,G(FQ \cap BC)$ are harmonic . $AD \perp BC$ lead to desired result .
Wed May 01, 2013 1:39 pm
Forum: Geometry
Topic: Prove P,Q,A,O concyclic
Replies: 2
Views: 1911

Let $E,F$ be the midpoints of $BD,DC$ respectively . $AD' \perp BC$ ($D' \in BC$). $E',F',P',Q'$ are midpoints of $BD',D'C,AB,AC$ respectively . Note that , $EE'=FF'$ Now $EE'=PP'\cos {B}$ and $FF'=QQ' \cos {C}$ so $\displaystyle \frac {PP'}{QQ'}=\frac{\cos {C}}{\cos {B}}=\frac {OP'}{OQ'}$ and $\ang... Tue Feb 26, 2013 8:24 pm Forum: Geometry Topic: Prove concyclic Replies: 4 Views: 2321 ### Re: Prove concyclic Let$AB \cap DC =H$Note that$D,G,C,H$build a harmonic range . So$\displaystyle \frac{DG}{CG}=\frac{DH}{CH}\Rightarrow MC^2=(DG-MG)(CG+MG)=MG.MH\Rightarrow DG.CG=MG.GH$Now$HB.HA=HC.HD=HG.HM\Leftrightarrow HC.(HC+CD)=(HC+CG).(HC+CM)\Leftrightarrow HC.CD=HC.CM+HC.CG+CG.CD\Leftright...
Sun Feb 03, 2013 5:45 pm
Topic: IMO Marathon
Replies: 184
Views: 63977

### Re: IMO Marathon

(unless I'm not being silly)

What is the difference between "circumcircle of triangle $ABC$" and $w$ ? :S
Sun Feb 03, 2013 4:37 pm
Topic: IMO Marathon
Replies: 184
Views: 63977

### Re: IMO Marathon

Problem $\boxed {28}$: Trapezoid $ABCD$, with $AB$ parallel to $CD$, is inscribed in circle $w$ and point $G$ lies inside triangle $BCD$. Rays $AG$ and $BG$ meet $w$ again at points $P$ and $Q$, respectively. Let the line through $G$ parallel to $AB$ intersect $BD$ and $BC$ at points $R$ and $S$, r...
Fri Feb 01, 2013 5:17 pm
Topic: Let us help one another preparing for BdMO national 2013
Replies: 12
Views: 6816

### Re: Let us help one another preparing for BdMO national 2013

Fahim Shahriar wrote:
And it doesn't have factor 5. Hence it's not divisible by 5.
How come ?
Fri Feb 01, 2013 12:25 pm