Search found 186 matches

by photon
Sun Feb 01, 2015 7:22 pm
Forum: College / University Level
Topic: Integrability
Replies: 3
Views: 4885

Re: Integrability

1. If a function doesn't "have" indefinite integral , then it doesn't "have" definite integral too because they are both same thing except the constant gets cancelled in definite integral and we get a definite value for 2 given limits . Now some functions (like $\ln(\ln x),x^x,\sin(\sin x)$ ) can n...
by photon
Fri Dec 19, 2014 11:57 am
Forum: Geometry
Topic: Side, Angle, and, (Ex)-Circle
Replies: 4
Views: 2226

Re: Side, Angle, and, (Ex)-Circle

$O$ is the centre of the excircle opposite to $A$ , to match with notations used in books , $O=I_A$
by photon
Tue Dec 16, 2014 7:07 pm
Forum: Social Lounge
Topic: Asking for a book
Replies: 3
Views: 2195

Re: Asking for a book

College Geometry by Nathan Altshiller-Court.
I haven't gone throughly this one , but I liked the contents , they cover nearly all important and useful things I suppose .
by photon
Fri Dec 05, 2014 4:14 pm
Forum: Junior Level
Topic: A surprising problem!!
Replies: 2
Views: 1877

Re: A surprising problem!!

This may help you ! :)
by photon
Tue Nov 25, 2014 3:22 pm
Forum: Geometry
Topic: powers are equal
Replies: 3
Views: 1799

powers are equal

$P$ is inside $\Delta ABC$ such that $AB,BC,CA$ are tangents to the circumcircles of $\Delta BPC,\Delta CPA,\Delta APB$ respectively . Extended $AP,BP,CP$ cuts the circumcircle of $\Delta ABC$ at $A',B',C'$ . Prove that power of $A$ (with respect to $\odot B'PC$ ),power of $B$ (wrt $\odot C'PA$ ),po...
by photon
Sat Nov 08, 2014 10:10 pm
Forum: Physics
Topic: Errors in Galileo’s Thought Experiment?
Replies: 2
Views: 2532

Re: Errors in Galileo’s Thought Experiment?

Logic isn't limited in common sense , it's process of applying principles which are known as truth . Yesterday's invention comes today handy for logicing . As I'm not a professional or even studied to that level yet , I have little experience regarding to scientific theory background . If logic shou...
by photon
Sat Oct 25, 2014 5:04 pm
Forum: Secondary Level
Topic: A circle through incenter
Replies: 2
Views: 2087

A circle through incenter

In $\Delta ABC$ , the incircle touches $AC,AB$ at the points $E,F$ respectively . $M$ is the midpoint of $EF$ . A circle $\omega$ (center $O$ ) is drawn through incenter $I$ and $M$ . Prove that $IO$ and $EF$ meet on the circle $\omega$ .

[edited. Thanks to Sowmitra .]
by photon
Tue Mar 04, 2014 12:43 pm
Forum: Geometry
Topic: Secondary Special Camp 2011: Geometry P 3
Replies: 3
Views: 2249

Re: Secondary Special Camp 2011: Geometry P 3

Zzzz via,you wrote:$\frac{BD}{CD}\times \frac{CE}{AE}\times \frac{AF}{FB}=1$.So,D,E,F collinear.Why! Here he used Menelaus' theorem , a theorem to prove collinearity . If three points lie on the three sides of a triangle (or their extensions) and are collinear , then they have this fraction relatio...
by photon
Mon Mar 03, 2014 11:08 pm
Forum: News / Announcements
Topic: ২০১৪ আঞ্চলিক পর্যায়ের প্রশ্ন
Replies: 4
Views: 5549

Re: ২০১৪ আঞ্চলিক পর্যায়ের প্রশ্ন

আঞ্চলিকের প্রশ্ন দেওয়াটা হয়তবা একটু বেশি সমস্যার যেহেতু প্রব্লেম বেশি । তবে জাতীয়রগুলা দেওয়া যায় । বিক্ষিপ্ত ভাবে টপিক না করে সবগুলা একসাথে দেওয়া অনেক সহায়ক । তাছাড়া অনেকেই থাকে যারা কিনা অংশ নেয় নাই , কিন্তু প্রব্লেম জানতে আগ্রহী , তারা ফোরাম থেকে নিতে পারে । (যদিও অলিম্পিয়াড সাইটে প্রশ্ন...
by photon
Sat Feb 22, 2014 10:38 pm
Forum: Algebra
Topic: x,y,z>1
Replies: 2
Views: 1500

Re: x,y,z>1

that was cool 8-) Let $x=a^2+1 , y=b^2+1 ,z=c^2+1 $, ($a,b,c>0$) then inequality becomes $\displaystyle \sqrt{a^2+b^2+c^2+3} \geq a+b+c$ $\Rightarrow a^2+b^2+c^2+3 \geq a^2+b^2+c^2+2ab+2bc+2ca$ $\Rightarrow \frac{3}{2}\geq ab+bc+ca $ We have $\sum \frac{1}{x}=2 \Rightarrow \sum \frac{1}{a^2+1}=2$ Le...