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If R is the circum radius of DeltaABC, t...

If R is the circum radius of `DeltaABC`, then A `(DeltaABC)`= . . .

A

`(abc)/(R)`

B

`(abc)/(4R)`

C

`(abc)/(3R)`

D

`(abc)/(2R)`

Text Solution

Verified by Experts

The correct Answer is:
B
In any `DeltaABC` we know that
Area of `Delta=(1)/(2)`bc sinA
`implies sinA=(2Delta)/(bc)` . . . (i)
`impliesR=(a)/(2sinA)` . . . (ii)
From Eqs. (i) and (ii), we have
`R=(a)/(2((2Delta)/(bc)))impliesR=(abc)/(4Delta)`
`thereforeDelta=A(DeltaABC)=(abc)/(4R)`
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