Well, as I am preparing for CAT 2012, so i thought it would be nice to share some out of the box things which i learn at my coaching classes. This might help you somewhere, and will be saved as an archive for my reference also. There is something very special kind of geometry I learned last week, and I am now exploring all the application part. The concept is very simple, and can be applied to any problem. Here is how I can explain it-

__The concept-__

It uses very simple principle of physics, which we have often observed in our daily life, see the figure below

__An Example-__

Question : – Consider the case below here are of small triangles contained in big triangle are known, now we have to find the area of whole triangle, I bet you can’t do this question in less than 10 minutes if you don’t know this method. Give it a try if you want to, before reading the solution.

Answer : – As we know base of triangle is in the same ratio as the areas are, when a line cuts triangle, hence the ratio of base will be same as ratio of areas.. Therefore, ratio of base-

Now, using mass geometry i can complete this triangle as shown below-

Here, numbers written are nothing but ratios of sides, we know the area and ratio of sides. Therefore, we can find unknown area of quadrilateral. Picture below shows the actual areas in squares and ratios of sides. Using this we can say that, ratio of area of triangle ABE and triangle BCE = (4+x)/(8+13) = 7/1, where x is area of quadrilateral.

Hi Prateek,

Please help me with this using Mass point Geometry.

In a triangle ABC, let E be a point on AB such that AE : EB = 1 : 3, D is a point on BC such that BD : DC = 4 : 1, and F is a point on ED joined such that EF : FD = 5 : 1. Show that

AG : GC = 4 : 1 and BF : FG = 17 : 7.

How to balance this problem to arrive at the answer ?

You haven't specified anything about point G.

hi prateek

i have a doubt here …

i didn't get this step

Answer : – As we know base of triangle is in the same ratio as the areas are, when a line cuts triangle, hence the ratio of base will be same as ratio of areas.. Therefore, ratio of base-

and how you simplified it later , could you elobarate it a bit ?

Ratio of base is known, you can re-distribute the weight according to this ratio to obtain corresponding weights.

how did you get the base as 7 and 14 i am still unable to figure this out ..pls explain …

Area of triangle are in ratio, 4:8, with the same base, Hence base will be in ratio 1:2, therefore 7:14(=1:2)

I divided it in terms of 7:14 because, 8+13 =21. Now we have to divide this 21 in ratio 1:2. Hence, 7:14

but why are bases being taken as 21 ..how are you assuming both to be the same is it given in the problem ? is it ok to assume like that ?

13+8 =21 This was an assumed base as per given ratio, I r distributed this base on another different base whose ratio is known as (1:2)

I didn't get any of these 🙁

Hi Prateek, how to solve quadrilateral problems with this concept?