Flag Magical Mathematics[Interesting Approach]> SOLVE THIS!!!...
question mark

the ratio of the area of the regular polygon of n sides circumscribed about a circle to the area of the regular polygon of equal no. of sides inscribed in the circle is 4:3.find the value of n

Shivam Bhagat , 13 Years ago
Grade 9
anser 3 Answers
sanatan sharma

Last Activity: 13 Years ago

let the polygon circumscribed about a circle be denoted by  PQRS........          & 

the polygon inscribed in the circle be    ABCD.........     and their centres be   O .

in polygon   PQRS........   let the mid-point of PQ be Y so OY is the radius of the circle.

 i recommend you to take pen and paper and do as directed .

let side PQ = x

angle POQ = 360/n     therefore   angle POY = 180/n

tan 180/n = x/2r                                     where r is the radius of the circle

x = 2r tan 180/n

area of triangle POQ = xr/2

area of triangle POQ = (2r2)/2 tan 180/n

area of polygon PQRS............= n (area of triangle POQ)                                              (1)-

in polygon ABCD..............

OB is the radius of the circle  , D is the mid-point of AB and angle AOB= 360/n

angle BOD = 180/n

sin 180/n = y/2r                                      where y is the length AB

y = 2r sin 180/n

similarly length OD = r cos 180/n

area of triangle AOB = y(OD)/2

area of triangle AOB = 2r2/2 (sin 180/n)( cos 180/n)

area of polygon ABCD........... = n(area of triangle AOB)

(area of polygon PQRS............)/(area of polygon ABCD...........) = 4/3

substituting the values we will get  a equation as

cos 180/n = √3/2

cos 180/n = cos 30

180/n = 30

therefore n =6

Sathya

Last Activity: 13 Years ago

Can u pls draw the diagram?

sanatan sharma

Last Activity: 13 Years ago

841_41804_circumscribed_WEB.gif

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments