From a point `O` inside a triangle `A B C ,` perpendiculars `O D ,O Ea n dOf` are drawn to rthe sides `B C ,C Aa n dA B ,` respecrtively. Prove that the perpendiculars from `A ,B ,a n dC` to the sides `E F ,F Da n dD E` are concurrent.

From a point O inside a triangle ABC , perpendiculars OD,OE and Of are drawn to rthe sides BC,CA and AB, respecrtively. Prove that the perpendiculars from A,B, and C to the sides EF, FD and DE are concurrent.

From a point O inside a triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB, respectively. Prove that the perpendiculars from A, B and C to the sides EF, FD and DE are concurrent

From a point O inside a triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB, respectively. Prove that the perpendiculars from A, B and C to the sides EF, FD and DE are concurrent

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

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

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that the (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .