Geometry. @iambatman

Question

parthkohli · Answer

In a triangle, how would you go about proving that the perpendicular bisectors of all the sides are concurrent?

parthkohli · Answer

This point of concurrency has a fascinating geometric interpretation. 

Hint: Circumcenter.

anonymous · Answer

|dw:1419172102619:dw| is this what you mean for circumcenter? 
Mhm I'll have to think about this proof for a bit, maybe write it out first...

parthkohli · Answer

I think you already have it with you.

parthkohli · Answer

AB, BC and AC are the chords of this circle.

The perpendicular bisector of a chord always passes through the centre of the circle.

Isn't that theorem cool? How would you prove THAT?

anonymous · Answer

Yes, exactly what I was thinking, but I'm not exactly sure how I will relate it to concurrency..

parthkohli · Answer

A perpendicular bisector will always pass through the center.

=> Three of them will always pass through the center.

anonymous · Answer

|dw:1419172920358:dw| BD = BC

So since we need three of them to pass through the centre, I can create a new segment between BP and CP?

anonymous · Answer

|dw:1419173143592:dw|