Help me! /sci/ (Math)

Hay you guys. Got a problem I gotta solve ... in 60mins.

Suppose a circle x^2+y^2=1. There's a line to cut it in half I'll call D that goes from (0,-1) to (0,1). There's also a point named (a,b) on the upper part of the circle (basicly a is positive). A is a line formed by relaying (0,-1) to (a,b) et B is a line formed by relaying (a,b) to (0,1).

I need to show using vectors that the triangle formed by A B D is necessarely a right triangle.

So you have 3 points, (0,1), (0,-1), and (a,b) where (a,b) has a>0 and -1<b<1.

You thus have 3 vectors (connecting each pair of points), these are: (a,b-1), (a,b+1), and (0,-2). The right angle will always be between the vectors (a,b-1) and (a,b+1). (draw it if you're not convinced). Two vectors are orthogonal (make a right angle) if their dot product is zero. Taking the dot product
(a,b-1).(a,b+1)=a^2+b^2-1
But (a,b) is on the circle a^2+b^2=1, so the dot product is 0, and the vectors are orthogonal.

>>2
Listen to this man, nice solution.

Thanks alot Anonymous. I had gotten to the point where I needed to do the dot product but I wasen't sure if I was on the right path! Thanks for the help :)

I'm feeling really keen, for some of that good ol' green

Marijuana MUST be legalized.