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In triangle ABC, AD and BE are the media...

In triangle `ABC, AD and BE` are the medians drawn through the angular points A and B respectively. `/_DAB=2/_ABE=36^@` and `AD=6` units then circumradius of the triangle is equal to

A

`(3-sqrt5)cosecC`

B

`(3+sqrt5)cosecC`

C

`2(3-sqrt5)cosecC`

D

`2(3+sqrt5)`cosecC

Text Solution

Verified by Experts

Applying sine rule in `Delta AGB`, we have
`rArrAB=(sin126^(@))/(sin18^(@))AG`
`AB=(cos36^(@))/(sin18^(@))xx2/3AD`
`rArrAB=(sqrt5+1)/(sqrt5-1)xx2/3xx6=2(3+sqrt5)`
Now, R`=c/(2sinC)rArrR=(3+sqrt5)cosecC`
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