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

Options

A. 1
B. 2
C. 3
D. none of these

Answer

C

Explanation

`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`