Mass Point Geometry by best teachers

Mass point geometry theorem for SSC CGL 

Definition :

Mass point geometry, colloquially known as mass points, is a geometry problem-solving technique which applies the physical principle of the center of mass to geometry problems involving triangles and intersecting cevians.
hough modern mass point geometry was developed in the 1960s by New York high school students  the concept has been found to have been used as early as 1827 by August Ferdinand Möbius in his theory of homogeneous coordinates.

Examples

Problem 1:

 In triangle ABC , E is on A so that CE=3AE  and

 F is on AB so that

 BF=3AF. If BE and CF intersect at o and line

 AO intersects BC at D,
compute OB/OE  and OD/OA.

Solution. We may arbitrarily assign the mass of point A to be 3

. By ratios of lengths, the masses at B and C must both be 1.

 By summing masses, the masses at E and F are both 4. 

Furthermore, the mass at O is 4+1=5, 

making the mass at D have to be 5-3=2 

Therefore OB/OE =4 and OD/OA=3/4. See diagram.

Problem 2.

In triangle ABC, D, E, and F are on BC, CA, and AB, respectively, so that
 AE=AF=CD=2, BD=CE=3, and BF=5.
 If DE and CF intersect at o,
compute  and .

Solution. As this problem involves a transversal, we must use split masses on point C. We may arbitrarily assign the mass of point A to be 15. 

By ratios of lengths, the mass at B must be 6 and the mass at c is split 10 towards A and 9 towards B.
By summing masses, we get the masses at

 D, E, and F to be 15, 25, and 21, respectively.


Therefore  and .

Diagram for solution to Problem Two

Learn from youtube :

Video 2

courtesy Amiya Sir :










Video 3.




Courtesy Abhinay Sir