O is any point inside a rectangle ABCD. Prove that `O B^2+O D^2=O A^2+O C^2`.

O is any point inside a rectangle ABCD.Prove that OB^(2)+OD^(2)=OA^(2)+OC^(2)

O is any point inside a rectangle ABCD. Prove that OB^(2)+OD^(2)=OA^(2)+OC^(2) . DEDUCTION In the given figure, O is a point inside a rectangle ABCD such that OB=6cm, OD=8 cm and OA=5 cm, find the length of OC.

A point O in the interior of a rectangle ABCD is joined with each of the vertices A,B,B,C and D. Prove that OB^(2)+OD^(2)=OC^(2)+OA^(2)

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)

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

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 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 a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

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\ a n d\ O is a point inside it. O A ,\ O B ,\ O C\ a n d\ 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)

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)