`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

O P Q R is a square and M ,N are the midpoints of the sides P Q and Q R , respectively. If the ratio of the area of the square to that of triangle O M N is lambda:6, then lambda/4 is equal to (a)2 (b) 4 (c) 2 (d) 16

Find the area of the square whose side length is m + n -q

If the middle points of the sides of a triangle are (-2,3),(4,-3),a n d(4,5) , then find the centroid of the triangle.

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

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

O is the circumcenter of A B Ca n dR_1, R_2, R_3 are respectively, the radii of the circumcircles of the triangle O B C ,O C A and OAB. Prove that a/(R_1)+b/(R_2)+c/(R_3),(a b c)/(R_3)

O A and O B are fixed straight lines, P is any point and P M and P N are the perpendiculars from P on O Aa n dO B , respectively. Find the locus of P if the quadrilateral O M P N is of constant area.

Let O be the origin, and O X x O Y , O Z be three unit vectors in the direction of the sides Q R , R P , P Q , respectively of a triangle PQR. If the triangle PQR varies, then the minimum value of cos(P+Q)+cos(Q+R)+cos(R+P) is: -3/2 (b) 5/3 (c) 3/2 (d) -5/3

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these