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# Help Wanted in Geometry

I face a lot of problem in solving a geometry problem. Most of the level 4 problems won't budge , let alone level 5. I have tried studying from books like Challenge and Thrill of Pre-College Mathematics and I could solve only the first few exercises of each geo. chapter. The approach to the problem doesn't strike to me, especially proving questions. Any advice, suggestion or a list of important theorems, maybe is welcome...

Note by Pankaj Joshi
2 years, 4 months ago

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Theorems are very important in solving geometry problems, But why don't you try to build up a theorem while solving? For example, (simple example) If one didn't know the law of cosines, he would solve a system of three equations to derive his desired answer, without knowing that he did derive a well-known theorem!

I don't mean that theorems are not important, But note that at this site, our main goal is to become more experienced and creative, so that this may lead us to create new ideas and solve unsolved problems...

My usual approach in solving geometry problems is to link all givens together, also try this:

remove one given from the question and try to solve again, you will notice at some step that something became harder, so this is a key to solve the problem, try to collect all keys and the correct time where you use them,(I always see this useful,try).

I hope I contributed in help . · 2 years, 3 months ago

Thank you, my friend.. · 2 years, 3 months ago

Welcome :) · 2 years, 3 months ago

Hey, Hasan, don't mean to be a bother, but did you see the comment I wrote on one of my problems mentioning you? I thought you could help me out a bit. If you can't, that's alright. Just making sure.

Link · 2 years, 3 months ago

yes John, but I didn't yet solve both problems :|

Whenever I solve them, I will be there for you:)

The first problem ( about system of differential equations), I can not solve it bcs I am not experienced with this topic.

The second one seems challenging and I am on it :) · 2 years, 3 months ago

Oh you mean the one with the badass chick in background pic? oh lol that's ok ;)

Take your time. Thank you, Hasan · 2 years, 3 months ago

Try learning single theorem one by one first, and then do the simple basic problems involving the theorem. After you're okay with that, try do some intermediate problems and stuffs. If you're done with more theorems, try do some geometry problems and slowly look at it, don't rush too much or trying to do it quick.

The best way to learn is to read the proofs. You can see the techniques of proving and might be able to use these for solving problems. I always do this every time when I start learning geometry.

During solving the geometry problems, try to get some information, and work with it. After some work, you might see what you need more, then you can look for them easily.

Even though I'm level 5, I still have a problem with lvl 5 problems too, because nowadays lvl 5 is freaking crazier than before. · 2 years, 3 months ago

Thanks a lot.. I have already started trying what you suggest. · 2 years, 3 months ago

@Aditya Raut @Ronak Agarwal @Calvin Lin ... · 2 years, 4 months ago

Actually, there is no problem in Geometry if you get it's TRICK. This trick is the part which makes a problem seemingly difficult, and if one notices that thing, then problem is easy. Talking of olympiad style problems, specially looking at the previous year RMO papers, I have always noticed that the most helpful strategy is that

$$\mathbf{1.}$$ Extract as much information as possible from the problem.

$$\mathbf{2.}$$ Think on which of the informations is going to be helpful.

$$\mathbf{3.}$$ People generally try proving things by high-figh theorems, but never forget to combine "Angle-chasing" with lengths. Angles many times make it easy.

$$\mathbf{4.}$$ Start with some of the things that you feel might help. Then, after you feel stuck at some step, start from the end, start getting things from the To Prove. Most of the times, you yourself reduce To Prove into a way simple thing and then CONNECT the approach from start with the one from end.

To know some needed (And in your words, important) theorems, the link that Shivang Jindal gives is one of the coolest.... · 2 years, 3 months ago

They had taught this in the INMOTC too :P · 2 years, 3 months ago

Thank you very much. · 2 years, 3 months ago

Try the problems more :), i also found the book very challenging when i started , but it becomes simple, if you try hard. Give atleast an hour to the problem, you are unable to do. :) · 2 years, 4 months ago

Yeah thanks... But thats the main problem...time... caught up with a lot of coaching work. Can you tell me where I can get the most commonly used theorems and their proofs? · 2 years, 4 months ago

I think, for basic you don't need anything more than, Ceva's theorem , menalus theorem, power of a point, radical axis,simson lines, common triangle centres(like centroid, circumcentre, incentre,ortho,gregonne), Euler's line. Just do a google search, on these topics. Or study from here: http://www.cut-the-knot.org/Curriculum/index.shtml · 2 years, 3 months ago

Thank you.. · 2 years, 3 months ago

Are you aiming for math olympiads, Pankaj. · 2 years, 4 months ago

I am aiming only for NSEP and NSEC but I shall feel more confident if I were better at geometry. BTW, you have leveled up in many subject, I see. Any help will be appreciated.. · 2 years, 4 months ago

If you prepare for geometry having mastery in topics like co-ordinate geometry and solution of triangles will help you the most, but still question based on maths olympiads will be out of your reach. · 2 years, 4 months ago