Which of the statements about the picture below is true? Choose 3.
postimg(.)org/image/qb71bjkjh/f11870c4/
A. F is the circumcenter of the triangle

Question

Which of the statements about the picture below is true? Choose 3. 
postimg(.)org/image/qb71bjkjh/f11870c4/ 
A. F is the circumcenter of the triangle<< 
B. F is the incenter of the triangle 
C. F is the point of concurrency of the perpendicular bisector of the sides of the triangle 
D. F is the point lf concurrent of the angle bisector of the angles of the triangle 
E. F is equipped from the angles of the triangle 
F. F is equidistant from the three sides of the triangle. 

I know A is one of the answers..

3mar · Answer

Can you upload your question's picture ?

sageee · Answer

https://postimg.org/image/yxz0n8bwp/38859214/

3mar · Answer

That makes sense now!

sageee · Answer

yes sorry about that! i thought i had uploaded it with the question..

3mar · Answer

No problem.

What did you get?
Any ideas?

sageee · Answer

i know one of the answers is a.
i don't think it's b but i'm not aure about the others

sageee · Answer

**sure

3mar · Answer

Are you familiar with that? http://www.mathopenref.com/triangleincenter.html http://www.mathopenref.com/trianglecircumcenter.html

sageee · Answer

yup

sageee · Answer

wouldn't the circle go outside og the triangle though?

3mar · Answer

- When the circle goes outside the triangle (touches its three vertex), so it is called "triangle's circumcircle".

- When the circle is confined into a triangle (its circumference is tangent to the triangle's sides from inside), so it is called "triangle's incircle".

sageee · Answer

oh ok, f is where all the segments meet so i guess that would be the incenter?

3mar · Answer

- When the circle goes outside the triangle (touches its three vertex), so it is called "triangle's circumcircle".....and its center (the circumcenter) is the point where the perpendicular bisectors of a triangle intersect....

and this is our case..

agree?

sageee · Answer

i agree

3mar · Answer

That is very good!

So A is with us....

3mar · Answer

- When a circle is confined into a triangle (its circumference is tangent to the triangle's sides from inside), so it is called "triangle's incircle", and its center, called the incenter, is the intersection of the angle bisectors.

Does F match this condition?

sageee · Answer

yes?

3mar · Answer

So $F$ is also the incenter of the triangle...
in other words, B is with us...agree?

sageee · Answer

yes i agree

sageee · Answer

is the last one D?

3mar · Answer

D is also correct and matches the point F....
but what about C?

sageee · Answer

Hmm C could be correct also but doesn't it need one more bisector

3mar · Answer

"doesn't it need one more bisector"
Do you mean that it needs to the third perpendicular bisector to meet $F$?

sageee · Answer

yeah

3mar · Answer

No, @Sageee the point of intersection of two indeed is the intersection of the three together!

and that is applied on the angles' bisectors and the perpendicular bisectors as well ...

sageee · Answer

Oh ok! But my question only has 3 answers so now I'm not sure which answers to choose..

3mar · Answer

WHich are these three?

sageee · Answer

A and B are for sure but I'm sure if I should choose C or D

3mar · Answer

I am sure that E and F are out.,.,.,., agree?

3mar · Answer

So I think it is D for sure!

sageee · Answer

Thank you so much for helping!

3mar · Answer

Don't mention it!
You are welcome!
I am here for your help.
Just if you need any help, don't hesitate to ask me and I will never be late for you In Sha' Allah.

3mar · Answer

Thank you for learning!
and
Thank you for the medal!