Search found 186 matches

Fri Oct 26, 2012 11:34 am
Forum: Geometry
Replies: 2
Views: 1072

let $OM,ON$ intersect $CD,AB$ at $N_1,M_1$. in $\Delta OCD$ , $ON$ is a median.$\displaystyle \frac{OC}{OD}=\frac{sin\angle NOD}{sin\angle NOC}=\frac{sin\angle BOM_1}{sin\angle AOM_1}=\frac{BM_1}{OB}\frac{OA}{AM_1}$ $\therefore \displaystyle \frac{OC}{OD}=\frac{OA.BM_1}{OB.AM_1}....... (1)$ ,similar...
Tue Oct 23, 2012 9:21 pm
Forum: Secondary Level
Topic: Seems easy
Replies: 4
Views: 1479

let $O$ is the intersecting point , ${\frac {OA}{OA_1}}={\frac {\Delta AOB}{\Delta A_1OB}}={\frac {2\Delta AOC_1}{2\Delta A_1OC}}={\frac {\frac {1}{2}. OA.OC_1 sin \angle AOC_1}{\frac {1}{2}.OA_1.OCsin \angle A_1OC}}={\frac {OA.OC_1}{OA_1.OC}}$ $\Rightarrow OC_1=OC$ ; $\therefore \Delta BOC_1=\Delta... Mon Oct 22, 2012 8:11 pm Forum: Higher Secondary Level Topic: perimeter of an isosceles tri. Replies: 1 Views: 3640 perimeter of an isosceles tri. in an isosceles triangle$ABC$($AB=AC$),$M$in a point on$BC$such that$BM=CM$.$\angle BXC=3\angle BAC$where$X$is a point on$AM$segment. if ,$AX=10,AM=11$, find the perimeter of the triangle . Fri Sep 14, 2012 8:12 pm Forum: Geometry Topic: SAMO 2012 Problem 2 Replies: 4 Views: 1473 Re: SAMO 2012 Problem 2 let,YZ=a.height of trapizoid$AYZB$is$1$. Area($AYZB$)=$\frac{1}{2}.1.(YZ+AB)=\frac{a+1}{2}$Area($AXB$)=$XYZ+AYZB=\frac{2}{3}+\frac{a+1}{2}=\frac{3a+7}{6}$. in similar triangle$XYZ,AXB\frac{a^2}{1}=\frac{XYZ}{AXB}=\frac{\frac{2}{3}}{\frac{3a+7}{6}}$,$\Rightarrow 3a^3+7a^2-4=0 \Rightarrow (...
Sat Aug 18, 2012 12:24 pm
Forum: Geometry
Topic: AIMO-5 2010 problem 1
Replies: 2
Views: 1008

Re: AIMO-5 2010 problem 1

my solution seems similar to Sanzeed's , but slight different for pic i guess.
Tue Jun 12, 2012 4:42 pm
Forum: Number Theory
Topic: $x^5-x=k^2$
Replies: 4
Views: 1290

$x^5-x=k^2$

find all positive integer $x$ with proof such that $x^5-x$ is a perfect square .
Sun May 27, 2012 11:29 am
Forum: Social Lounge
Topic: অভিনন্দন !
Replies: 12
Views: 4566

Re: অভিনন্দন !

congratulation for all!!!! no wish for luck just 10 gallons felix felicis for each one .....
Wed May 23, 2012 3:42 pm
Forum: National Math Camp
Topic: geometry might be easy
Replies: 2
Views: 1360