Search found 57 matches
- Tue Apr 18, 2017 7:06 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 44111
Re: Beginner's Marathon
Could you please assert the last line more clearly?
- Tue Apr 18, 2017 6:28 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 44111
Re: Beginner's Marathon
Problem 14:Let the incircle of triangle ABC touch BC at D. Let,DT be a diameter of the circle.If AT meets BC at M,prove that BD=CM.
- Tue Apr 18, 2017 6:16 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 44111
Re: Beginner's Marathon
Let us denote by $ABC$,the area of $\bigtriangleup ABC$. From geometric proportion,$\frac{PD}{AD} = \frac{PBC}{ABC}$ as the bases of $\bigtriangleup ABC$ and $\bigtriangleup PBC$ are the same.This case works for $\bigtriangleup PAC$ and $\bigtriangleup PAB$ as well.So,we concurr that $\frac{PD}{AS} ...
- Sat Apr 08, 2017 12:31 pm
- Forum: Junior Level
- Topic: geomerty
- Replies: 10
- Views: 8264
Re: geomerty
<FAD itself measures 100 degree,then how can you concurr that AD=DF?I think you did not consider triangle DAF. ..According to your construction,<BCE=140 as it is supplementary to <ACB. Therefore,as CF=CD, <FCD=160 and <DFC=<DFA merely measures 10...check out your angle chasing...
- Sat Mar 18, 2017 7:14 pm
- Forum: Number Theory
- Topic: Equation
- Replies: 1
- Views: 2290
Equation
x^2+xy+y^2=(x+y+3)^3/27,find all(x,y)
- Fri Mar 03, 2017 8:01 pm
- Forum: Geometry
- Topic: IGO 2016 Elementary/4
- Replies: 8
- Views: 6099
Re: IGO 2016 Elementary/4
It is just the official solution....is there any unique technique to solve that?
- Sat Feb 25, 2017 12:33 pm
- Forum: Geometry
- Topic: IGO 2016 Elementary/4
- Replies: 8
- Views: 6099
Re: IGO 2016 Elementary/4
Isn't BC the diameter of the circumcircle?
- Thu Feb 23, 2017 4:58 pm
- Forum: Divisional Math Olympiad
- Topic: BDMO REGIONAL 2015
- Replies: 1
- Views: 2637
Re: BDMO REGIONAL 2015
Note that the distinct numbers are repeated according to their intrinsic values.Find their summation noticing that the summation of a distinct pair is equal to the square of that distinct pair.Find the remainder which shows that the division upon a number by 3 leaves the same remainder as it does up...
- Thu Feb 23, 2017 4:49 pm
- Forum: Geometry
- Topic: BDMO regional 2015
- Replies: 4
- Views: 4506
Re: BDMO regional 2015
For problem 10,note that SP=7 units because ST is the perpendicular bisector of triangle SPR.Apply angle bisector theorem taking PT=RT=a and PQ=b,find b=18a/7.Then apply Stewart's theorem;which mentions 324a^2/7+36a^2=16(49+63),derive a point, (24a)^2=112^2;a=14/3.Therefore,PR=2a=28/3 which takes th...
- Wed Feb 22, 2017 8:18 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO NATIONAL JUNIOR 2013/07
- Replies: 2
- Views: 2817
Re: BDMO NATIONAL JUNIOR 2013/07
As per me,there won't be any fantabulous integer because at a point 1 may arrive as a fantabulous integer but it is not as 0 is not a positive integer.For this reason,the number of such integers will be 0.