`pdotC_(21)+qdotC_(22)+rdotC_(23)=` `(a) 0` (b) `triangle` (c) `-triangle` (d) `4`

qdotM_(12)+ydotM_(22)+mdotM_(32)= (a) 0 (b) triangle (c) -triangle (d) None of these

xdotC_(21)+ydotC_(22)+zdotC_(23) is (a)0 (b) delta (c) -delta (d) None of these

A triangle whose one angle is more than 90^0 is called (a) a scalene triangle (b) a right triangle (c) an acute triangle (d) an obtuse triangle

The three points (-2,2)(8,-2),a n d(-4,-3) are the vertices of (a) an isosceles triangle (b) an equilateral triangle (c) a right-angled triangle (d) none of these

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

If Delta=|(a_(11), a_(12), a_(13) ),(a_(21), a_(22), a_(23)),(a_(31), a_(32), a_(33))| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by (A) a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) (B) a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) (C) a_(21)A_(11)+a_(22)A_(12)+a_(23)A_(13) (D) a_(11)A_(11)+a_(21)A_(21)+a_(31)A_(31)

If the medians of a triangle A B C intersect at G , show that a r( triangle A G B)=a r( triangle A G C)=a r( triangle B G C)=1/3a r( triangle A B C) . GIVEN : triangle A B C such that its medians A D ,B E and C F intersect at G . TO PROVE : a r(triangle A G B)=a r( triangle B G C)=a r(triangle A G C)=1/3a r(triangle A B C)

Triangles A B C and DBC are on the same base B C with A, D on opposite side of line B C , such that a r(triangle A B C)=a r( triangle D B C) . Show that B C bisects A D .

Diagonals A C and B D of a trapezium A B C D with A B || C D intersect each other at O . Prove that ar ( triangle A O D)=a r( triangle B O C) .

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( triangle O A B)=a r(triangle O B C)