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 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 E^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

From a point O in the interior of a A B C , perpendiculars O D ,\ O E and O F are drawn to the sides B C ,\ C A and A B respectively. Prove that: (i) A F^2+B D^2+C E^2=O A^2+O B^2+O C^2-O D^2-O E^2-O F^2 (ii) A F^2+B D^2+C E^2=A E^2+C D^2+B F^2

A point O in the interior of a rectangle A B C D is joined with each of the vertices A ,\ B ,\ C and D . Prove that O B^2+O D^2=O C^2+O A^2

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 O B^2+O D^2=O A^2+O C^2 .

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

If O is the circumcentre of /_\ A B C and O D_|_B C , prove that /_B O D=/_A

Let O be a point inside a triangle A B C such that /_O A B=/_O B C=/_O C A=omega , then show that: Cos e c^2omega=cos e c^2A+cos e c^2B+cos e c^2C

Let O be a point inside a triangle A B C such that /_O A B=/_O B C=/_O C A=omega , then show that: cotomega=cotA+cotB+cot C Cos e c^2omega=cos e c^2A+cos e c^2B+cos e c^2C