IIT JEE , AIEEE Forum - Mathematics , Trignometry

m.viddya

Q.The ratio of areas of regular hexagons which are inscribed in a triangle of radius r and circumscribed to the same circle is?

1. 1:2

2. 2:3

3. 3:4

4. 1:3

anandghegde

what do you mean by triangle of radius r?

anandghegde

so many questions at a single stretch? Looks like you have posted your entire homework here.....

sandeepramesh

or it could be that the particular person in question is presently revising this chapter

m.viddya

well...well..well...no solution still/?

computer001

wat is a triangle of radius r precisely??

computer001

area oh hexagon inscribed in incircle =6*1/2*r^2cos30

area of hexagon ins in circumcircle=6*1/2*R^2cos30

so to find ratio v need r/R
where r is inradius R is circumrad
r=4RsinA/2sinB/2sinC/2
so ratio is 4sinA/2sinB/2sinC/2

computer001

if u r askin min value then it is 1/2

Greatdreams

Question is wrong she means that the hexagon is within the circle in the first case and then in the next case , the circle is circumscribed by the hexagon

So in the first case lets take that the hexagon is within the circle.
so 6 equilateral triangles are formed,

hence area = 6 *

3/4 r^2

for the second one area = 6 *

3/4 a^2 where a = 2r/

3

So ratio of areas = 3 : 4

So triangle part has to be excluded.

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