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The area of an acute triangle ABC is Del...

The area of an acute triangle ABC is `Delta`, the area of its pedal triangle is 'p' , where `cos B=(2p)/(Delta)` and `sin B=(2sqrt(3)p)/(Delta)`. The value of `8(cos^(2)A cos B+cos^(2)C)` is

A

1

B

2

C

3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`Delta =2R^(2)` sin A sin B sin C
Similarly, `p=2((R )/(2))^(2)` sin 2 A sin 2B sin 2 C
`=4R^(2)` sin A sin B sin C cos C cos B cos C
Now `(p)/(Delta)=2` cos A cos B cos `C ge (1)/(4)`
where `cos^(2)B+sin^(2)B=1 rArr (p)/(Delta)=(1)/(4)`
`rArr Delta ABC` is equilateral
`rArr 8(cos^(2)Acos B+cos^(2)C)=3`
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