IIT JEE , AIEEE Forum - Mathematics , Algebra

Mr.IITIAN007

Ratio of diameters of incircle to circumcircle of a regular polygon is d_i:d_c.Then what is the number of diagonals of the polygon?

deepak_agarwal

we noe dat r=a/(2tan

/n), where r=radius of incentre,a=side length,n=no. of sides

R=a/(2sin(pi/n)),where R=radius of circumcentre

di/dc=[sin(pi/n)]/ [tan(pi/n)]

n=pi/cos^-1(di/dc)

by inspection

n=no. of sides D=no of diagonals

3 0

4 2

5 5

6 9

7 14

8 20

ven v derive d formula v get

no. of diagonals=(n-3)(n/2)

no of diagonals=pi/(cos^-1di/dc-3)((pi/cos^-1di/dc)/2)

Mr.IITIAN007

You are right sir.But can you please solve the answer when d_i=

6+

4 and d_c=4.The answer should come 54.