Triangles: Prove that OA + OB + OC = OP + OQ + OR

[physics]

If O is any point on the triangle ABC and P,Q,R are midpoints of the sides AB,BC,CA respectively, prove that OA + OB + OC = OP +OQ + OR

Does the result hold if O is any point outside the triangle? Prove it?

 

[Deleted member 4993]

Re: TRIANGLES

If O is any point on the triangle ABC and P,Q,R are midpoints of the sides AB,BC,CA respectively, prove that OA + OB + OC = OP +OQ + OR
...Does the result hold if O is any point outside the triangle? Prove it?

This is a well known corollary - almost any geometry book has it.

Please show your work and indicate exactly where you are stuck - so that we know where to begin to help.

 

[physics]

i solved for the sides using similar right triangles and that way showed that they were not equal