i didnt get what you(zzz) meant by whoever can post any problems .
So this wont just be geometry marathon?!
Geometry Marathon v1.0
Re: Geometry Marathon v1.0
Can't anyone solve Problem 4?? It is easy I guess. 
Anyway, I shall post problem in January, now this month. Sorry...
Anyway, I shall post problem in January, now this month. Sorry...
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Re: Geometry Marathon v1.0
Anyone can post any gemotry problem here:)tushar7 wrote:i didnt get what you(zzz) meant by whoever can post any problems .
So this wont just be geometry marathon?!
Every logical solution to a problem has its own beauty.
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(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)
Re: Geometry Marathon v1.0
Couldn't solve Problem 4 using transformation. 
An appreciable fact is found out but proof isn't complete.
However, I am posting another problem.
Problem 5:
Line $l$ is tangent to the circumcircle of acute triangle $\triangle ABC$ at $B$. Let $K$ be the projection of the orthocenter of $\triangle ABC$ onto line $l$, and let $L$ be the midpoint of $AC$. Show that $\triangle BKL$ is isosceles.
Someone explain me what does 'projection on the orthocenter of triangle ABC onto line l' mean.
Check the question I added before question 3. Help me by proving if it's true or disprove if it's false.
If projection means reflection the question is incorrect. But I guess it doesn't.
An appreciable fact is found out but proof isn't complete.However, I am posting another problem.
Problem 5:
Line $l$ is tangent to the circumcircle of acute triangle $\triangle ABC$ at $B$. Let $K$ be the projection of the orthocenter of $\triangle ABC$ onto line $l$, and let $L$ be the midpoint of $AC$. Show that $\triangle BKL$ is isosceles.
Someone explain me what does 'projection on the orthocenter of triangle ABC onto line l' mean.
Check the question I added before question 3. Help me by proving if it's true or disprove if it's false.
If projection means reflection the question is incorrect. But I guess it doesn't.
"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter
Re: Geometry Marathon v1.0
Please don't post new problem before someone solves the previous one. Unless, the problem is unsolvable. We can also set some rule:
If the problem goes unsolved for two days the poster of the problem will post a solution, and then anyone may post a new problem. In case the person who posted the problem is not available the problem must be tagged as [UNSOLVED] and then anyone may post a new problem.
If the problem goes unsolved for two days the poster of the problem will post a solution, and then anyone may post a new problem. In case the person who posted the problem is not available the problem must be tagged as [UNSOLVED] and then anyone may post a new problem.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Geometry Marathon v1.0
Please please reply the two questions in coloured font. @Admin or anybody who can.
"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter
Re: Geometry Marathon v1.0
Cabri II says $P,Q$ and $R$ are collinear in problem 1 ! But I couldn't prove it..TIUrmi wrote:Please please reply the two questions in coloured font. @Admin or anybody who can.
Every logical solution to a problem has its own beauty.
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(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)
Re: Geometry Marathon v1.0
My proving used that fact but I could prove this part.
"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter
Re: Geometry Marathon v1.0
Uh...I feel you guys are really stuck.
Projection meant perpendicular projection I guess.
Projection meant perpendicular projection I guess.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Geometry Marathon v1.0
Should I close this marathon?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.