In a `DeltaABC`, the distance of sides `BC, AC and AB` from circumcentre are `d_1, d_2 and d_3` respectively (where `a,b& c` are length of sides in usual notation) If `(a/d_1+b/d_2+c/d_3)=k(abc)/(d_1 d_2 d_3)` , then the value of 'k' is `lambda/mu,lambda,mu in N` and are comprime then

If ( a times b)*(c times d)=(a*c)(b*d)+k(a.d)(b.c) then the value of k is

In Delta ABC as shown,XX_(1)=d_(1);XX_(2)=d_(2);XX_(3)=d_(3) and X is the centre of the circumscribed circle around the Delta ABC,a,b and c as usual are the sides BC,CA and AB respectively.If lambda((a)/(d_(1))+(b)/(d_(2))+(c)/(d_(3)))=(abc)/(d_(1)d_(2)d_(3)), then the value of 'lambda'' is equal to

The coordinates of the mid points of sides AB, BC and CA of A B C are D(1,2,-3),\ E(3,0,1)a n d\ F(-1,1,-4) respectively. Write the coordinates of its centroid.

The coordinates of the mid points of sides AB, BC and CA of A B C are D(1,2,-3),\ E(3,0,1)a n d\ F(-1,1,-4) respectively. Write the coordinates of its centroid.

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Detla ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is (a) 1 (b) 2 (c) 3 (d) 4

If D is the mid point of side BC of a triangle ABC such that vec A B+ vec A C=lambda\ vec A D , write the value of lambdadot

If the distance of the plane x - y + z + lambda = 0 from the point (1, 1, 1) is d_1 and the distance of this point from the origin is d_2 and d_2d_2 = 5 then find the value of lambda .

Let f,g,h be the lengths of the perpendiculars from the circumcenter of the Delta ABC on the sides BC,CA and AB respectively.If (a)/(f)+(b)/(g)+(c)/(h)=lambda(abc)/(fgh), then the value of 'lambda' is (B) (1)/(2) (B) (1)/(2) (D) (1)/(2) (D) 2