`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

A B C D parallelogram, and A_1a n dB_1 are the midpoints of sides B Ca n dC D , respectivley . If vec AA_1+ vec A B_1=lambda vec A C ,t h e nlambda is equal to a. 1/2 b. 1 c. 3/2 d. 2 e. 2/3

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is (a)4:1 (b) 2:1 (c) 8:3 (d) 7:3

In a triangle A B CifB C=1a n dA C=2, then what is the maximum possible value of angle A ?

The centroid of a triangle ABC is at the point (1,1,1) . If the coordinates of A and B are (3,-5,7) and (-1,7,-6) , respectively, find the coordinates of the point C.

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that the (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

If an a triangle A B C , b=3ca n d C-B=90^0, then find the value of tanB

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If angleGAC = (pi)/(3) and a = 3b , then sin C is equal to