La ricerca ha trovato 8 risultati

da stergiu
19 set 2009, 09:34
Forum: Geometria
Argomento: Nice but not easy !
Risposte: 4
Visite : 2187

Nice but not easy !

Let ABC an acute triangle. The circle with diameter the altitude BD meets sides

AB,BC at K,L respectively. The tangents of this circle at K,L meet at M.Prove that

line BM bisects segment AC.

Babis
da stergiu
15 set 2009, 09:53
Forum: Geometria
Argomento: triangolo
Risposte: 3
Visite : 1682

Have you any non metric solution to this problem ?

Of cource, it is easy to find that $ 3(c-a) = 2(m_c-m_a) $ .Then using the median formulae , we find a=c.

Μπάμπης
da stergiu
06 set 2009, 20:40
Forum: Geometria
Argomento: Isosceles triangle
Risposte: 2
Visite : 1469

Excellent :D !!!

Babis
da stergiu
04 set 2009, 23:05
Forum: Geometria
Argomento: Isosceles triangle
Risposte: 2
Visite : 1469

Isosceles triangle

Well, a nice problem for beginers with olympiads is the following:

Problem

The incircle of a triangle ABC touches BC at D. Let E be the projection of B on the bisector of angle A. If M is the midpoint of side BC, prove that the triangle MDE is isosceles.

Enjoy it - Babis
da stergiu
04 set 2009, 10:12
Forum: Geometria
Argomento: Parallel segments - not difficult
Risposte: 5
Visite : 1982

Nice problem stergiu :wink: Let \alpha,\beta,\gamma be the angles \angle CAB,\angle ABC,\angle BCA . First case: M belongs to the arc AB wich not contains C. \angle MNA = \angle MBA because they lie on the same arc. Since M is on the bisector of the external angle B, \angle MBA = \dfrac{(\angle CAB...
da stergiu
02 set 2009, 23:01
Forum: Geometria
Argomento: Parallel segments - not difficult
Risposte: 5
Visite : 1982

Parallel segments - not difficult

After having seen and loged in at your wonderfull site, I put a simple geometry problem for students of class 10-12. . Problem The bisector of the internal angle A and the bisector of the external angle B of a triangle ABC meet the circumcircle of the triangle at points M,N.If I is the incenter of ...
da stergiu
02 set 2009, 20:05
Forum: Olimpiadi della matematica
Argomento: Mediterranean olympiad
Risposte: 2
Visite : 2025

Thank you very much ! I visited these links.

To be more acurate, I was looking for the problem for year 2009, but nobody has them. Probably the competition did not appear this year.
If I learn something new, I will let you know !

Regards - Babis
da stergiu
01 set 2009, 18:53
Forum: Olimpiadi della matematica
Argomento: Mediterranean olympiad
Risposte: 2
Visite : 2025

Mediterranean olympiad

Hallo to all math friends in italy ! I'd like to ask you if you know the problems and solutions for maditerranean olympiads (years 2000 - 2009), or a link(in italian, english, spanish ect). I was asked for the problems by a greek student who prepares himself for IMO , but at moment I can not be in c...