In the figure, CD, AE and BF are one-third of their respective sides. It follows that `AN_2 : N_2 N_1 : N_1 D= 3 : 3 : 1` and similarly for lines BE and CF. Then the area of triangle `N_1 N_2 N_3`. in term of`Delta ABC` is

G is the centroid of triangle A B Ca n dA_1a n dB_1 are rthe midpoints of sides A Ba n dA C , respectively. If "Delta"_1 is the area of quadrilateral G A_1A B_1a n d"Delta" is the area of triangle A B C , then "Delta"//"Delta"_1 is equal to a.3/2 b. 3 c. 1/3 d. none of these

G is the centroid of triangle A B Ca n dA_1a n dB_1 are rthe midpoints of sides A Ba n dA C , respectively. If "Delta"_1 is the area of quadrilateral G A_1A B_1a n d"Delta" is the area of triangle A B C , then "Delta"//"Delta"_1 is equal to a. 3/2 b. 3 c. 1/3 d. none of these

G is the centroid of triangle A B Ca n dA_1a n dB_1 are rthe midpoints of sides A Ba n dA C , respectively. If "Delta"_1 is the area of quadrilateral G A_1A B_1a n d"Delta" is the area of triangle A B C , then "Delta"//"Delta"_1 is equal to a. 3/2 b. 3 c. 1/3 d. none of these

tan^(-1)n ,tan^(-1)(n+1) and tan^(-1)(n+2),n in N , are the angles of a triangle if n= 1 (b) 2 (c) 3 (d) None of these

If for n sequences S_(n)=2(3^(n)-1) , then the third term is

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1) cm, then area of the triangle is 1/2(sqrt(3)+1)s qdotu n i t s area of the triangle is 1/2(sqrt(3)-1)s qdotu n i t s

If the coordinates of the mid-points of the sides of a triangle are (1,1),(2,-3)a n d(3,4) . Find its centroid.

The circle inscribed in the triangle ABC touches the side BC, CA and AB in the point A_(1)B_(1) and C_(1) respectively. Similarly the circle inscribed in the Delta A_(1) B_(1) C_(1) touches the sieds in A_(2), B_(2), C_(2) respectively and so on. If A_(n) B_(n) C_(n) be the nth Delta so formed, prove that its angle are pi/3-(2)^-n(A-(pi)/(3)), pi/3-(2)^-n(B-(pi)/(3)),pi/3-(2)^-n(C-(pi)/(3)). Hence prove that the triangle so formed is ultimately equilateral.

The circle inscribed in the triangle ABC touches the side BC, CA and AB in the point A_(1)B_(1) and C_(1) respectively. Similarly the circle inscribed in the Delta A_(1) B_(1) C_(1) touches the sieds in A_(2), B_(2), C_(2) respectively and so on. If A_(n) B_(n) C_(n) be the nth Delta so formed, prove that its angle are pi/3-(2)^-n(A-(pi)/(3)), pi/3-(2)^-n(B-(pi)/(3)),pi/3-(2)^-n(C-(pi)/(3)). Hence prove that the triangle so formed is ultimately equilateral.

tan^(-1)n,tan^(-1)(n+1) and tan^(-1)(n+2),n in N are the angles of a triangle if n= (a) 1(b)2(c)3(d) None of these