A plane makes intercepts `O A ,O Ba n dO C` whose measurements are `a,b` and `c` on the `O X ,O Ya n dO Z` axes. The area of triangle `A B C` is a. `1/2(a b+b c+c a)` b. `1/2a b c(a+b+c)` c. `1/2(a^2b^2+b^2c^2+c^2a^2)^(1//2)` d. `1/2(a+b+c)^2`

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

In a triangle A B C ,(r_1+r_2)/(1+cosC) is equal to (2a b)/(c"Delta") (b) ((a+b))/(c"Delta") (a b c)/(2"Delta") (d) (a b c)/("Delta"^2)

If sides of triangle ABC are a,b and c such that 2b=a+c then (b)/(c)>(2)/(3)( b) (b)/(c)>(1)/(3)(b)/(c)<2 (d) (b)/(c)<(3)/(2)

If a b+b c+c a=0 , then what is the value of (1/(a^2-b c)+1/(b^2-c a)+1/(c^2-a b)) ? (a) 0 (b) 1 (c) 3 (d) a+b+c

If a,b and c are the side of a triangle,then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c) is 3 (b) 9(c)6(d)1

If ' O ' is the circum centre of the A B C and R_1,\ R_2,\ R_3 are the radii of the circumcircle of triangle O B C ,\ O C A\ a n d\ O A B respectively then a/(R_1)+b/(R_2)+c/(R_3) has the value equal to (a b c)/(2R^3) (b) (R^3)/(a b c) (c) (4)/(R^2) (d) (a b c)/(R^3)