## Search found 217 matches

Thu Jan 24, 2013 6:18 pm
Forum: Secondary Level
Topic: Solve this congruence equation
Replies: 2
Views: 1525

### Re: Solve this congruence equation

Still not interested. $SIGH$
btw,Happy Birthday.
Wed Jan 23, 2013 1:59 pm
Topic: IMO Marathon
Replies: 184
Views: 62189

I propose a new rule that anyone who posts a solution of a problem must certainly post another problem.Or we'll have to wait for someone's grace. Problem $\boxed{22}$:Let $ABCD$ be a parallelogram.A variable line $l$ passing through the point $A$ intersects the rays $BC$ and $CD$ at points $X$ and $... Wed Jan 23, 2013 1:29 pm Forum: International Mathematical Olympiad (IMO) Topic: IMO Marathon Replies: 184 Views: 62189 ### Re: IMO Marathon I Love Ratio. :mrgreen:$\frac{SC}{SB}=\frac{SA}{SC}\Longrightarrow \frac{SP}{SB}=\frac{SA}{SP}\triangle{SPB} \sim \triangle{SAP}$and$\triangle{SCB} \sim \triangle{SAC}\frac{AP}{BP}=\frac{AS}{PS}=\frac{AS}{CS}=\frac{AC}{BC}$from alternate segment theorem,$\frac{MK}{MP}=\frac{AC}{AP}$an... Wed Jan 23, 2013 10:03 am Forum: International Mathematical Olympiad (IMO) Topic: IMO Marathon Replies: 184 Views: 62189 ### Re: IMO Marathon I wish every geometry problems were as easy and as beautiful as this. Wed Jan 23, 2013 9:56 am Forum: International Mathematical Olympiad (IMO) Topic: IMO Marathon Replies: 184 Views: 62189 ### Re: IMO Marathon Problem 21:Let$ABC$be a triangle with$P$in its interior(with$BC \neq AC$).The lines$AP,BP,CP$meet$\odot{ABC}$again at$K,L,M$.The tangent line at$C$intersects$AB$at$S$.Show that from$SC=SP$it follows that$MK=ML$Source: IMO 2010-Problem: 4 Tue Jan 22, 2013 10:13 pm Forum: Higher Secondary Level Topic: Secondary and Higher Secondary Marathon Replies: 127 Views: 57096 ### Re: Secondary and Higher Secondary Marathon Problem$\boxed{34}$:$ABCD$is a cyclic quadrilateral.$E$and$F$are variable points on sides$AB$and$CD$respectively such that$\displaystyle \frac{AE}{BE}=\frac{CF}{DF}$.$\; P$is a point on the segment$EF$such that$\displaystyle \frac{EP}{PF}=\frac{AB}{CD}$.Show that$\displaystyle \frac{...
Tue Jan 22, 2013 8:10 pm
Topic: IMO Marathon
Replies: 184
Views: 62189

### Re: IMO Marathon

Solution $\boxed {19}$:Same as Tahmid.
Solution $\boxed {20}$:Actually $APIE$ is concyclic .Which implies $\angle {A}$=$90$
Problem $19$ seemed harder to me than problem $20$.
Tue Jan 22, 2013 1:21 pm
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 57096

### Re: Secondary and Higher Secondary Marathon

If we draw a circle centering at $A$ with radius $AC$ as $CD^2=AD.BD$ it holds that $D$ lies on the radical axis of the two circles.And $DK$ is the radical axis.And we now that the radical axis is perpendicular to the line joining the centres of the concerning circles.The result follows.
Tue Jan 22, 2013 12:59 pm
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 57096

### Re: Secondary and Higher Secondary Marathon

Well,Adib notice that $AK=AC$ he said.
Mon Jan 21, 2013 12:07 am
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 57096

### Re: Secondary and Higher Secondary Marathon

Well,this is problem 3 of geomtry problem set of BDMC 2012.