# Quantitative Aptitude > Geometry

 Refresher Test 2 - Geometry Discuss Refresher Test - Geometry Discuss

Practice Tests
 Practice Test - Geometry Discuss

Parallel lines

Free Online Preparation for CAT with Minglebox e-CAT Prep. Cover basic concepts of Geometry under Quantitative Aptitude for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts.

Two lines lying in a plane are said to be parallel if they never meet.

Polygons

A closed figure, bounded by finite number of line segments, all lying in the same plane, is known as polygon.

Sum of interior angles of a polygon having 'n' sides, =

Sum of exterior angles of a polygon = 360 ( irrespective of number of sides)

Triangles

A triangle is a polygon formed by 3 line segments joined end to end.

Sum of interior angles of a triangle = 180

In any given triangle sum of 2 interior angles is equal to the third remote angle.

AD is the median of triangle, then

G is the centroid of the triangle .Centroid of a triangle divides the median AD in the ratio 2:1

Angle Bisector Theorem

If AD is the bisector of the the angle ABC then AD divided the side BC in the ratio

ie

Circle Theorem

If AC is a chord of circle then angle ABC subtended by the chord at a point B on the circle is equal to

to angle subtended at point 0 lying in the same segment ie ∟ABC = ∟ADC. Also angle ABC is half of

angle AOC.

Alternate Segment Theorem

If XTB is a tangent to the circle then ∟ATB =∟ACT.

Area of a triangle =

=

where

Area of a circle of radius r =

Area of a square of side

Length of diagonal of square =

Area of rectangle of length l and breath b= lb

volume of cube of edge length

length of cube =

Volume of sphere of radius r =

Volume of hemisphere of radius r =

Surface area of cube =

Surface area of sphere =

Surface area of hemisphere =

SOLVED EXAMPLES

QUESTION

The sum of the areas of two circles, which touch each other externally, is 153 . If the sum of their radii is 15, find the ratio of the larger to the smaller radius.

(1) 4

(2) 2

(3) 3

(4) none of these.

SOLUTION

Let the radii of the 2 circles be and , then = 15 (given)

and = (given)

= 153

solving we get, = 12 and = 3

ratio of the larger radius to the smaller one is 12 : 3 = 4 : 1 hence option (1) is the answer.

QUESTION

In the adjoining figure, points A, B, C and D lie on the circle. AD= 24 and BC = 12. what is the ratio of the area of CBE to that of the triangle ?

(1) 1:4

(2) 1:2

(3) 1:3

(4) data insufficient.

SOLUTION

In and , ∟ CBA = ∟ CDA.

( a chord of a circle subtends equal angel at all points on the circumference, lying in the same segment)

similarly ∟ BCD = ∟ BAD and ∟ BEC = ∟ AED

Therefore ( AAA similarity rule)

Now

Hence hence option b).

QUESTION

and are two concentric circles while BC and CD are tangents to at point P and respectively. AB to the circle , which of the following is true?

(1)

(2)

(3)

(4) data insufficient

SOLUTION

l ( cp) = l (cr) ( since tangents drawn from the same point are equal)

hence l(BC) = l( CD) ( points P and R are midpoints of BC and CD as OP is ┴BC and OR ┴ CD)

Therefore m( arc BXC) = m(arc CYD)

But m(arc BXC ) = ( ∟ABC) = ( tangent secant theorem)

therefore m(arc BZD) =

Therefore m(BCD) =

Hence m∟PCR =

m∟POR = 2m ∟PQR = (angle at center)

m∟OPC + m∟ORC =

Hence m∟POR + m∟PCR =

Therefore

QUESTION

Two circles of radius 3 units and 4 units are at some distance such that length of the transverse common tangents and the length of their direct common tangents are in the ratio 1: 2 . What is the distance between the centres of those circles?

(1) units

(2) units

(3)        8 units

(4)        cannot be determined .

SOLUTION

Let x = distance between the centres of the circles.

T= length of the transverse common tangent.

D = length of direct common tangent.

And = 4 units and = 3 units

then, t = --------------- 1)

also d =

------------------- 2)

=

Since

units

hence

hence x =

from 1) and 2 ) we get

d = 2t

d = 8 units

hence answer is option 2 ).

 Refresher Test 2 - Geometry Discuss Refresher Test - Geometry Discuss

 Practice Test - Geometry Discuss

amit39967 : need a bunch of 1000 questions

ankur36512 : i m not able to understand the concepts .. can any one help me to solve this..

shalu34890 : for deepak5949- height is same and base is double hence 1:2(example-2)

caroline13463 : concepts r short & crisp..really gud..but ans to second illustration is wrong

heena1405 : they r really very good concepts......really rocks...thanks.....

arthi9429 : really very knowledgeable ques.

ankita7231 : thanksssss alotttttttt

astha6214 : sir !geometry is one of my favourite! and this material is awesome!! if u jus similarly provide us with algebra revision concepts it wud b of great ..great help!! u c i was about to purchase a buk for the same but u can save my time so plzzzzz...plz provide d same 4 algebra..! i will b highly obliged!!

vikrant4516 : unbeleivable

dear_bks : its really nice...

saranya2768 : the ans. fr practice test Q.11 is 50

saranya2768 : in the practice test..ques no. 9 has error..i.e 516 is typed as 576

arush3101 : wah kya concepts hein!!!!!!!!!!!!

amit8752 : u people r very very nice ones
i thank u all from the core of my heart

shri3834 : second problem answer is wrong.....
It is 1:4
area=1/2*a*b*sinC
so ratio consists of product of 2 sides...since angles are equal in both triangles.
so ratio areas is 2*2=4 i.e 1:4....

sonia4863 : give me a very good qns

shilpigarg3707 : its really a very helpful concept for every student and its will help to understand the cat question.Thankxxxxxxxxxxxxxxxxxxxxxx for this

deepak3520 : sir
plz give me much more topic of DI,function mean QA,and passsage of english

dev3780 : its absorbing material

nitin481 : deepak5949 u r absolutely correct. In similar triangles ratio of area is equal to squares of ratio f their sides.

ishan3887 : thank god i got this .....really good concepts

vcchoudhary : very very unbelievable concept. Really, this is very knowledgable info for me

ankit4877 : gd questions to open our mind,,,,

deepak5949 : Solution to second illustration of geometry is incorrect.
The answer should be 1:4 and not 1:2 because ratio of area is required to be calculated.

nitesh7369 : some times we are alone and one way is opened its like that for me thaksssssssssssssssss

bhavya7710 : Really like the material on geometry.

: material is good but tests are not workin ...it would be really helpful if the problem is sorted out asap

ankit4877 : really gd concepts....

jagdeep9051 : its good...

ajeet8632 : I AM VERY HAPPY.THANXXXXXX

sapana8470 : this is very helpfull for me.

athipathi9725 : super upppuuuuuuuu