`O` is any point in the interior of ` A B Cdot` Prove that `A B+A C > O B+O C` `A B+B C+C A > O A+O B+O C` `O A+O B+O C >1/2(A B+B C+C A)`

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

A B C D IS A PARALLELOGRAM AND O is any point in its interior. Prove that: a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(^(gm)A B C D) Given: A parallelogram A B C D\ a n d\ O is a point in its interior. To Prove: a r\ (\ A O B)+\ a r( C O D)=a r\ ( B O C)+a r( A O D)

In figure, O is a point in the interior of a triangle ABC, O D_|_B C ,O E_|_A C and O F_|_A B . Show that (i) O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2 (ii) A F^2+B D^2+C E^2=A W^2+C D^2+B F^2

In fig., O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that:- O A^ 2 + O B^ 2 + O C^ 2 − O D^ 2 − O E^ 2 − O F^ 2 = A F^ 2 + B D^ 2 + C E^ 2

In A B C ,\ \ /_A=60o . Prove that B C^2=A B^2+A C^2-A B.A C .

A B C D is a rectangle with O as any point in its interior. If a r ( A O D)=3 c m^2a n d a r ( B O C)=6 c m^2, then area of rectangle A B C D is: 9c m^2 (b) 12 c m^2 (c) 15 c m^2 (d) 18 c m^2

A B C D is a trapezium in which A B C D . The diagonals A C and B D intersect at O . Prove that (i) A O B C O D (ii) If O A=6c m , O C=8c m , Find: (A r e a ( A O B))/(A r e a ( C O D)) (b) (A r e a ( A O D))/(A r e a ( C O D))

If O\ a n d\ O^(prime) are circumcentre and orthocentre of \ A B C ,\ t h e n\ vec O A+ vec O B+ vec O C equals a. 2 vec O O ' b. vec O O ' c. vec O ' O d. 2 vec O ' O

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. GIVEN : A rectangle A B C D and O is a point inside it. O A ,O B ,O C and O D have been joined.. TO PROVE : a r(A O D)+a r( B O C)=a r( A O B)+a r( C O D) CONSTRUCTION : Draw E O F A B and L O M A Ddot

If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then O vecA + O vec B + O vec C + vec (OD) =