[sf-lug] py class: need math help!

[Charles-Henri Gros]

Alex Kleider wrote:
> 
> I need some help with what seems to be elementary math/trig:
> 
> Take a pencil and piece of paper and try to stay with me:
> 
> We start at C for center of circle and based on that center 
> draw an arc of radius r from A to B such that the angle ACB is equal to twice theta
> bisect our angle with a line from C to D at the midpoint of the arc.
> it intersects AB at E
> Now I've been assuming that triangles DEB and BEC were similar and therefore
> knowing ED and EB I was solving for CB (the radius.)
> i.e : tan theta = ED / EB
>    and radius = CB = EB/sin theta

I don't think DEB and BEC are similar:
CBD is isoceles (CD = CB = r), so (CDB) = (CBD) = (180 - theta) / 2

(EDB) = (CDB); furthermore (BED) = 90 (right angle)

So: (EDB) = (180-theta)/2 = 90 - theta/2
    (BED) = 90
    (EBD) = 180 - (EDB) - (BED) = theta/2

And: BE = r sin(theta)


-- 
Charles-Henri