Quick geometry concepts for CAT 2008

Geometry, as a topic is very improtant from the perspective of CAT or any graduate MBA exam. However, there are a few resources available the crisply presents the key concepts and some uniqwue fundas involved. I am trying to present such concepts for CAT 2008 as many of our friends are appreaing for AIMCAT also. I hope these concepts will be of some help and you may use them as a checklist of concepts. However, i will not elaborate on the concepts. Reader are encouraged to cross verify the concepts and post a feedback to us. Cheers, MadeITsimple

Concepts that i am writing are not related with any specific flow. I noted down the points as they apprea while studying.

Concepts:

Sum of internal angle of polygon = (n-2) x 180

Each angle of polygon = (n-2) x 180 / n ; where n is the number of sides of give polygon.

Area of equilateral triangle = root 3 /4 x (side)^2 

Area of isosceles tringle = b/4 root (4a^2 - b^2)

If triangle is right angled, then the length of base and perpendicular side will differ by 1 unit in measurement.

In right angled trinagle, base = Perpendicular side = hyp/ root 2

Angle bisector theorem:

AB x AC - BDxDC = AD^2

Sum of exterior angles of any polygon is = 360

No of side of a polygon = 360/measure of one ext. angle

Sum of two sides of a trinagle has to be always grater than the third side.

Difference between any two sides of tringle has to be always lesser than the third side.

Ext. angle  is equal to sum of interior angles not adjacent to it.

 For equilateral trinalge,

Area = (root 3) / (4) x (side)^2

Quick Tip: To get the height of an equilateral triangle, divide the base of the forumla i.e. ”4″ by power of side, i.e 2. Now what you get is : root 3/2 x side

Circum Radius: side/root 3

In radius : side/ 2root 3

Triangle - Median Concept:

2 x (Median)^2 + 2 x (1/2 third side)^2 = Sum of other two sides

In a convex quadrilateral inscribed in a circle,

For the above figure we have (P x R) + (Q x S) = AC x BD 

Hope it helps..

Regards,

Ameya